Geometric Phases, Noise and Non-adiabatic Effects in Multi-level Superconducting Systems
NASA Astrophysics Data System (ADS)
Berger, S.; Pechal, M.; Abdumalikov, A. A.; Steffen, L.; Fedorov, A.; Wallraff, A.; Filipp, S.
2012-02-01
Geometric phases depend neither on time nor on energy, but only on the trajectory of the quantum system in state space. In previous studies [1], we have observed them in a Cooper pair box qubit, a system with large anharmonicity. We now make use of a superconducting transmon-type qubit with low anharmonicity to study geometric phases in a multi-level system. We measure the contribution of the second excited state to the geometric phase and find very good agreement with theory treating higher levels perturbatively. Furthermore, we quantify non-adiabatic corrections by decreasing the manipulation time in order to optimize our geometric gate. Geometric phases have also been shown to be resilient against adiabatic field fluctuations [2]. Here, we analyze the effect of artificially added noise on the geometric phase for different system trajectories. [1] P. J. Leek et al., Science 318, 1889 (2007) [2] S. Filipp et al., Phys. Rev. Lett. 102, 030404 (2009)
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately. PMID:26738875
NASA Astrophysics Data System (ADS)
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately. PMID:26738875
Non-adiabatic effect on quantum pumping
NASA Astrophysics Data System (ADS)
Uchiyama, Chikako
2014-03-01
We study quantum pumping for an anharmonic junction model which interacts with two kinds of bosonic environments. We provide an expression for the quantum pumping under a piecewise modulation of environmental temperatures with including non-adiabatic effect under Markovian approximation. The obtained formula is an extension of the one expressed with the geometrical phase(Phys. Rev. Lett. 104,170601 (2010)). This extension shows that the quantum pumping depends on the initial condition of the anharmonic junction just before the modulation, as well as the characteristic environmental parameters such as interaction strength and cut-off frequencies of spectral density other than the conditions of modulation. We clarify that the pumping current including non-adiabatic effect can be larger than that under the adiabatic condition. This means that we can find the optimal condition of the current by adjusting these parameters. (The article has been submitted as http://arxiv.org/submit/848201 and will be appeared soon.) This work is supported by a Grant-in-Aid for Scientific Research (B) (KAKENHI 25287098).
Geometric phase shifting digital holography.
Jackin, Boaz Jessie; Narayanamurthy, C S; Yatagai, Toyohiko
2016-06-01
A new phase shifting digital holographic technique using a purely geometric phase in Michelson interferometric geometry is proposed. The geometric phase in the system does not depend upon either optical path length or wavelength, unlike dynamic phase. The amount of geometric phase generated is controllable through a rotating wave plate. The new approach has unique features and major advantages in holographic measurement of transparent and reflecting three-dimensional (3D) objects. Experimental results on surface shape measurement and imaging of 3D objects are presented using the proposed method. PMID:27244436
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
NASA Astrophysics Data System (ADS)
Alijah, Alexander; Kokoouline, Viatcheslav
2015-10-01
Vibrational energies and wave functions of the triplet state of the H3+ ion have been determined. In the calculations, the ground and first excited triplet electronic states are included as well as the most important part of the non-Born-Oppenheimer coupling between them. The diabatization procedure proposed by Longuet-Higgins is then applied to transform the two adiabatic ab initio potential energy surfaces of the triplet-H3+ state into a 2 × 2 diabatic matrix. The diabatization takes into account the effect of the geometrical phase due to the conical intersection between the two adiabatic potential surfaces. The results are compared to the calculation involving only the lowest adiabatic potential energy surface of the triplet-H3+ ion and neglecting the geometrical phase. The energy difference between results with and without the non-adiabatic coupling and the geometrical phase is about one wave number for the lowest vibrational levels.
Nonlinear effects generation in non-adiabatically tapered fibres
NASA Astrophysics Data System (ADS)
Palací, Jesús; Mas, Sara; Monzón-Hernández, David; Martí, Javier
2015-12-01
Nonlinear effects are observed in a non-adiabatically tapered optical fibre. The designed structure allows for the introduction of self-phase modulation, which is observed through pulse breaking and spectral broadening, in approximately a centimetre of propagation using a commercial telecom laser. These devices are simple to fabricate and suitable to generate and control a variety of nonlinear effects in practical applications because they do not experience short-term degradation as previously reported approaches. Experimental and theoretical results are obtained, showing a good agreement.
Non-adiabatic perturbations in multi-component perfect fluids
Koshelev, N.A.
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
On geometric interpretation of the berry phase
NASA Astrophysics Data System (ADS)
Katanaev, M. O.
2012-03-01
A geometric interpretation of the Berry phase and its Wilczek-Zee non-Abelian generalization are given in terms of connections on principal fiber bundles. It is demonstrated that a principal fiber bundle can be trivial in all cases, while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.
The geometric phase in quantum physics
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase.
Geometric phase in vacuum condensates, application to Unruh effect and to quantum thermometer
NASA Astrophysics Data System (ADS)
Capolupo, Antonio
2015-07-01
We report on the recent results revealing the presence of the geometric phase in all the systems characterized by particle creation from vacuum and vacuum condensates. This fact makes the geometric phase a useful tool in the study and the understanding of disparate phenomena. Its possible application ranges from the dynamical Casimir effect to the Hawking effect, from quantum field theory in curved space to the study of CP and CPT symmetries, from the graphen physics to superconductivity and to the Bose Einstein condensate. Here, we consider the possibility of the detection of the Unruh effect and of the fabrication of a very precise quantum thermometer. We analyze the Mukunda-Simon phase for a two level atom system and consider two case: 1) atoms accelerated in electromagnetic field, and 2) atoms interacting with thermal states. The Mukunda-Simon phase generalizes the Berry phase to the case of non-cyclic and non-adiabatic evolutions; therefore it represents a more useful instrument in experimental implementations with respect to the Berry phase.
The Geometric Phase of Stock Trading
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote. PMID:27556642
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote. PMID:27556642
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-01-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity. PMID:26224326
The geometric phase controls ultracold chemistry
NASA Astrophysics Data System (ADS)
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH-->H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
The geometric phase controls ultracold chemistry.
Kendrick, B K; Hazra, Jisha; Balakrishnan, N
2015-01-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity. PMID:26224326
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O_{2} reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
Detection of geometric phases in superconducting nanocircuits
NASA Astrophysics Data System (ADS)
Falci, Giuseppe; Fazio, Rosario; Palma, G. Massimo; Siewert, Jens; Vedral, Vlatko
2000-09-01
When a quantum-mechanical system undergoes an adiabatic cyclic evolution, it acquires a geometrical phase factor in addition to the dynamical one; this effect has been demonstrated in a variety of microscopic systems. Advances in nanotechnology should enable the laws of quantum dynamics to be tested at the macroscopic level, by providing controllable artificial two-level systems (for example, in quantum dots and superconducting devices). Here we propose an experimental method to detect geometric phases in a superconducting device. The setup is a Josephson junction nanocircuit consisting of a superconducting electron box. We discuss how interferometry based on geometrical phases may be realized, and show how the effect may be applied to the design of gates for quantum computation.
Non-adiabatic perturbations in Ricci dark energy model
Karwan, Khamphee; Thitapura, Thiti E-mail: nanodsci2523@hotmail.com
2012-01-01
We show that the non-adiabatic perturbations between Ricci dark energy and matter can grow both on superhorizon and subhorizon scales, and these non-adiabatic perturbations on subhorizon scales can lead to instability in this dark energy model. The rapidly growing non-adiabatic modes on subhorizon scales always occur when the equation of state parameter of dark energy starts to drop towards -1 near the end of matter era, except that the parameter α of Ricci dark energy equals to 1/2. In the case where α = 1/2, the rapidly growing non-adiabatic modes disappear when the perturbations in dark energy and matter are adiabatic initially. However, an adiabaticity between dark energy and matter perturbations at early time implies a non-adiabaticity between matter and radiation, this can influence the ordinary Sachs-Wolfe (OSW) effect. Since the amount of Ricci dark energy is not small during matter domination, the integrated Sachs-Wolfe (ISW) effect is greatly modified by density perturbations of dark energy, leading to a wrong shape of CMB power spectrum. The instability in Ricci dark energy is difficult to be alleviated if the effects of coupling between baryon and photon on dark energy perturbations are included.
Genuine vacuum-induced geometric phases
NASA Astrophysics Data System (ADS)
Wang, Minghao; Wei, L. F.; Liang, J. Q.
2015-04-01
Since a pioneer work on vacuum-induced Berry phase (VIBP) was done by Fuentes-Guridi et al. [Phys. Rev. Lett. 89 (2002) 220404], much attention has been paid to the geometric phase effects of vacuum field. However, all the so-called VIBPs investigated previously are not purely vacuum-induced (i.e. the nonvacuum components of the field are also involved). In this paper, we discuss how to deliver geometric phases from the evolution of a genuine vacuum field in a standard cavity quantum electrodynamics (QED) system. First, we design a cyclic evolution of an atom-field system with the atom being initially prepared at the excited state and the field at the genuine vacuum. Then, we calculate the geometric phases acquired during such a cyclic evolution. It is found that such geometric phases are really induced by an evolution of the genuine vacuum field. Specifically, our generic proposal is demonstrated with both the one- and two-mode Jaynes-Cummings model interactions (JCM).
Classical nuclear motion coupled to electronic non-adiabatic transitions
Agostini, Federica; Abedi, Ali; Gross, E. K. U.
2014-12-07
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Classical nuclear motion coupled to electronic non-adiabatic transitions
NASA Astrophysics Data System (ADS)
Agostini, Federica; Abedi, Ali; Gross, E. K. U.
2014-12-01
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Geometric-phase atom optics and interferometry
NASA Astrophysics Data System (ADS)
Zygelman, B.
2015-10-01
We illustrate how geometric gauge forces and topological phase effects emerge in atomic and molecular systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices including a velocity sieve, a component in mass spectrometers, for neutral atoms. We introduce and outline a possible experimental setup that demonstrates topological interferometry for neutral spin-1/2 systems. For that two-level system, we study the transition from Abelian to non-Abelian behavior and explore its relation to the molecular Aharonov-Bohm effect.
Geometric stability of topological lattice phases
Jackson, T. S.; Möller, Gunnar; Roy, Rahul
2015-01-01
The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311
Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics
NASA Astrophysics Data System (ADS)
Albert, Julian; Kaiser, Dustin; Engel, Volker
2016-05-01
Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O2more » reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.« less
Geometric phase effects in ultracold chemistry
NASA Astrophysics Data System (ADS)
Hazra, Jisha; Naduvalath, Balakrishnan; Kendrick, Brian K.
2016-05-01
In molecules, the geometric phase, also known as Berry's phase, originates from the adiabatic transport of the electronic wavefunction when the nuclei follow a closed path encircling a conical intersection between two electronic potential energy surfaces. It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. It arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. Illustrative results are presented for the O+ OH --> H+ O2 reaction and for hydrogen exchange in H+ H2 and D+HD reactions. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and ARO MURI Grant No. W911NF-12-1-0476 (N.B.).
Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions.
Menzeleev, Artur R; Bell, Franziska; Miller, Thomas F
2014-02-14
We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically non-adiabatic dynamics of the system. KC-RPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, time-reversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of position-representation RPMD by enabling the description of non-adiabatic transitions between states associated with general, many-electron wavefunctions and by accurately describing deep-tunneling processes across asymmetric barriers. We demonstrate that KC-RPMD yields excellent numerical results for a range of model systems, including a simple avoided-crossing reaction and condensed-phase electron-transfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force. PMID:24527896
Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions
Menzeleev, Artur R.; Bell, Franziska; Miller, Thomas F.
2014-02-14
We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically non-adiabatic dynamics of the system. KC-RPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, time-reversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of position-representation RPMD by enabling the description of non-adiabatic transitions between states associated with general, many-electron wavefunctions and by accurately describing deep-tunneling processes across asymmetric barriers. We demonstrate that KC-RPMD yields excellent numerical results for a range of model systems, including a simple avoided-crossing reaction and condensed-phase electron-transfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force.
Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics
White, Alexander J.; Gorshkov, Vyacheslav N.; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics
NASA Astrophysics Data System (ADS)
White, Alexander J.; Gorshkov, Vyacheslav N.; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-01
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Synchronous particle and non-adiabatic capture
Kats, J.M.
1988-01-01
In the theory of particle longitudinal motion, a classical definition of synchronous particle (synchronous energy, phase, and orbit) assumes that there is a one-to-one correspondence between the guiding magnetic field and the frequency of the accelerating electrical field. In practice, that correspondence may not be sustained because of errors in the magnetic field, in the frequency, or because sometimes one does not want to keep that relationship for some reason. In this paper, a definition of synchronous particle is introduced when the magnetic field and the frequency are independent functions of time. The result is that the size and shape of the bucket (separatrix) depends not only on the field rate of change but also on the frequency rate of change. This means, for example, that one can have a stationary bucket even with a rising field. Having the frequency, in addition to the field and voltage, as parameters controlling the shape and the size of the bucket, it is shown how to decrease particle losses during injection and capture. 2 refs., 2 figs.
Analysis of geometric phase effects in the quantum-classical Liouville formalism
Ryabinkin, Ilya G.; Izmaylov, Artur F.; Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 ; Hsieh, Chang-Yu; Kapral, Raymond
2014-02-28
We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.
Toroidal Precession as a Geometric Phase
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Nonadiabatic fluctuation in the measured geometric phase
NASA Astrophysics Data System (ADS)
Ai, Qing; Huo, Wenyi; Long, Gui Lu; Sun, C. P.
2009-08-01
We study how the nonadiabatic effect causes the observable fluctuation in the “geometric phase” for a two-level system, which is defined as the experimentally measurable quantity in the adiabatic limit. From the Rabi exact solution to this model, we give a reasonable explanation to the experimental discovery of phase fluctuation in the superconducting circuit system [P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Göppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraf, Science 318, 1889 (2007)], which seemed to be regarded as the conventional experimental error.
Non-adiabatic Dynamics of Molecules in Optical Cavities
NASA Astrophysics Data System (ADS)
Kowalewski, Markus; Bennett, Kochise; Mukamel, Shaul
Molecular systems coupled to optical cavities are promising candidates for a novel kind of photo chemistry. Strong coupling to the vacuum field of the cavity can modify the potential energy surfaces opening up new reaction pathways. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime. The possibilities for photo chemistry are demonstrated for a set of model systems representing typical situations found in molecules. Supported by the Alexander von Humboldt Foundation.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficientmore » as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.« less
Design of geometric phase measurement in EAST Tokamak
NASA Astrophysics Data System (ADS)
Lan, T.; Liu, H. Q.; Liu, J.; Jie, Y. X.; Wang, Y. L.; Gao, X.; Qin, H.
2016-07-01
The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Meanwhile, the influences of some controllable parameters on geometric phase are evaluated. The feasibility and challenge of distinguishing geometric effect in the POINT signal are also assessed in detail.
Geometric Phase of a Transported Oscillator
Dittirich, W.
2004-02-25
An oscillator constrained to a plane that is transported along some surface will rotate by an angle dependent only on the path and the surface, not on the speed at which it is transported. This is thus an example of a geometric phase. We analyze this phase using the methods of parallel transport. This concept plays a key role in General Relativity, but it can also be applied in classical mechanics. The Foucault pendulum can be seen as an application of this analysis, where the surface is a sphere and the curve is a line of constant latitude. In view of some considerable confusion and erroneous treatments in the recent literature, we here present a rather simple way for visualizing the motion of the Foucault pendulum using concepts that are based on Frenet's formulae and the methods of parallel displacement.
When do we need to account for the geometric phase in excited state dynamics?
Ryabinkin, Ilya G.; Joubert-Doriol, Loïc; Izmaylov, Artur F.
2014-06-07
We investigate the role of the geometric phase (GP) in an internal conversion process when the system changes its electronic state by passing through a conical intersection (CI). Local analysis of a two-dimensional linear vibronic coupling (LVC) model Hamiltonian near the CI shows that the role of the GP is twofold. First, it compensates for a repulsion created by the so-called diagonal Born–Oppenheimer correction. Second, the GP enhances the non-adiabatic transition probability for a wave-packet part that experiences a central collision with the CI. To assess the significance of both GP contributions we propose two indicators that can be computed from parameters of electronic surfaces and initial conditions. To generalize our analysis to N-dimensional systems we introduce a reduction of a general N-dimensional LVC model to an effective 2D LVC model using a mode transformation that preserves short-time dynamics of the original N-dimensional model. Using examples of the bis(methylene) adamantyl and butatriene cations, and the pyrazine molecule we have demonstrated that their effective 2D models reproduce the short-time dynamics of the corresponding full dimensional models, and the introduced indicators are very reliable in assessing GP effects.
Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials
Li Xuan; Brue, Daniel A.; Blandon, Juan D.; Parker, Gregory A.; Kendrick, Brian K.
2011-02-14
We present a method for properly treating collinear conical intersections in triatomic systems. The general vector potential (gauge theory) approach for including the geometric phase effects associated with collinear conical intersections in hyperspherical coordinates is presented. The current study develops an introductory method in the treatment of collinear conical intersections by using the phase angle method. The geometric phase angle, {eta}, in terms of purely internal coordinates is derived using the example of a spin-aligned quartet lithium triatomic system. A numerical fit and thus an analytical form for the associated vector potentials are explicitly derived for this triatomic A{sub 3} system. The application of this methodology to AB{sub 2} and ABC systems is also discussed.
Cao, Jun; Liu, Li-Hong; Fang, Wei-Hai; Xie, Zhi-Zhong; Zhang, Yong
2013-04-01
Azobenzene is one of the most widely used photoactive units and recently an ethylene-bridged azobenzene (BAB) was reported to have greatly enhanced conversion efficiency, quantum yield, and other favorable properties. As the first step towards exploring its photo-switchable character in real systems, we report here a systematic study on the photoisomerization dynamics between trans (E) and cis (Z) isomers in the gas phase and the CH3OH solution, using ab initio based surface hopping and molecular dynamics, which is the first report of dynamics simulation to reveal the environmental effects on BAB photoreactions. Results show that while the relatively faster S1 relaxation of the photo-induced E → Z process is only mildly affected by the solvent effect, the relatively slower S1 relaxation of the reverse reaction becomes even slower in the solution compared to the gas phase. The subsequent S0 dynamics from the conical intersection between S1 and S0 (CI_E) to Z is accelerated in solution compared to the gas phase because of avoided re-crossing to the S1 state, while the S0 dynamics from the conical intersection between S1 and S0 (CI_Z) to E are basically the same in both phases. Overall, the solvent effect was found to enhance the back-and-forth photo-switch efficiency between the Z and E isomers compared to the gas phase, while the quantum yields are reduced. But the solution yields of both the forward and backward photoreactions are still around 0.4. Therefore, BAB may have good photo-responsive properties if used as a photoactive unit in real systems. These results will facilitate future experimental and theoretical studies in this area to help design new azobenzene derivatives as photoactive units in biological processes, nanoscale devices, and photo-responsive materials. PMID:23574226
Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states
NASA Astrophysics Data System (ADS)
Humeniuk, Alexander; Mitrić, Roland
2016-06-01
A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.
Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states.
Humeniuk, Alexander; Mitrić, Roland
2016-06-21
A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states. PMID:27334155
Turbulent Density Variations in Non-Adiabatic Interstellar Fluids
NASA Astrophysics Data System (ADS)
Higdon, J. C.; Conley, Alex
1998-05-01
Analyses of radio scintillation measurements have demonstrated (e.g., Rickett, ARAA, 28, 561, 1990) the existence of ubiquitous turbulent density fluctuations in the interstellar medium. Higdon (ApJ, 309, 342, 1986) and Goldreich and Sridhar (ApJ, 438, 763 1995) have modeled successfully these density variations as entropy structures distorted by convection in anisotropic magnetohydrodynamic turbulent flows. However, the interstellar medium is a heterogeneous non-adiabatic fluid whose thermal properties result ( Field, ApJ, 142, 531 1965) from a balance of heating and cooling rates. The effect of the non-adiabatic nature of interstellar fluids on the properties of turbulent cascades to small scales has not been considered previously. We find that in thermally stable fluids that the required balance of heating and cooling decreases the amplitudes of entropy structures independently of their spatial scale. Consequently, we show that if the time scale for turbulent flows to cascade to small scales is significantly greater than the cooling time of an interstellar fluid, the generation of turbulent denisty density variations at large wave numbers is greatly suppressed. Such results constrain possible values for the turbulent outer scale in models of interstellar turbulent flows.
Geometric phases for mixed states of the Kitaev chain.
Andersson, Ole; Bengtsson, Ingemar; Ericsson, Marie; Sjöqvist, Erik
2016-05-28
The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation. PMID:27091168
Digital polarization holography advancing geometrical phase optics.
De Sio, Luciano; Roberts, David E; Liao, Zhi; Nersisyan, Sarik; Uskova, Olena; Wickboldt, Lloyd; Tabiryan, Nelson; Steeves, Diane M; Kimball, Brian R
2016-08-01
Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed. PMID:27505793
Quantum phases and dynamics of geometric phase in a quantum spin chain under linear quench
NASA Astrophysics Data System (ADS)
Sarkar, S.; Basu, B.
2012-12-01
We study the quantum phases of anisotropic XY spin chain in presence and absence of adiabatic quench. A connection between geometric phase and criticality is established from the dynamical behavior of the geometric phase for a quench induced quantum phase transition in a quantum spin chain. We predict XX criticality associated with a sequence of non-contractible geometric phases.
Spatial Non-Cyclic Geometric Phase in Neutron Interferometry
Filipp, Stefan; Hasegawa, Yuji; Loidl, Rudolf; Rauch, Helmut
2005-01-01
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by some of the authors to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism. The extension to non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere. The theoretical treatment comprises the cyclic geometric phase as a special case, which is confirmed by experiment. PMID:27308131
Geometric phase in a flat space for electromagnetic scalar waves.
Luis, Alfredo
2006-08-15
We show the existence of a fundamental geometric phase for classical electromagnetic fields arising after cyclic paths in a plane instead of a sphere. This phase is dispersive, is not related to polarization, distinguishes geometrical from wave optics, and can be easily measured in an interferometric arrangement. PMID:16880859
Non-adiabatic dynamics of molecules in optical cavities
NASA Astrophysics Data System (ADS)
Kowalewski, Markus; Bennett, Kochise; Mukamel, Shaul
2016-02-01
Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces thereby opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use quantities readily accessible from quantum chemistry codes like the adiabatic potential energy surfaces and dipole moments to carry out wave packet simulations in the dressed basis. The implications for photochemistry are demonstrated for a set of model systems representing typical situations found in molecules.
Observational tests of non-adiabatic Chaplygin gas
Carneiro, S.; Pigozzo, C. E-mail: cpigozzo@ufba.br
2014-10-01
In a previous paper [1] it was shown that any dark sector model can be mapped into a non-adiabatic fluid formed by two interacting components, one with zero pressure and the other with equation-of-state parameter ω = -1. It was also shown that the latter does not cluster and, hence, the former is identified as the observed clustering matter. This guarantees that the dark matter power spectrum does not suffer from oscillations or instabilities. It applies in particular to the generalised Chaplygin gas, which was shown to be equivalent to interacting models at both background and perturbation levels. In the present paper we test the non-adiabatic Chaplygin gas against the Hubble diagram of type Ia supernovae, the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background and the linear power spectrum of large scale structures. We consider two different compilations of SNe Ia, namely the Constitution and SDSS samples, both calibrated with the MLCS2k2 fitter, and for the power spectrum we use the 2dFGRS catalogue. The model parameters to be adjusted are the present Hubble parameter, the present matter density and the Chaplygin gas parameter α. The joint analysis best fit gives α ≈ - 0.5, which corresponds to a constant-rate energy flux from dark energy to dark matter, with the dark energy density decaying linearly with the Hubble parameter. The ΛCDM model, equivalent to α = 0, stands outside the 3σ confidence interval.
Geometric Phase for Adiabatic Evolutions of General Quantum States
Wu, Biao; Liu, Jie; Niu, Qian; Singh, David J
2005-01-01
The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.
Measurement of a vacuum-induced geometric phase
Gasparinetti, Simone; Berger, Simon; Abdumalikov, Abdufarrukh A.; Pechal, Marek; Filipp, Stefan; Wallraff, Andreas J.
2016-01-01
Berry’s geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing. PMID:27386533
Geometric phase for open quantum systems and stochastic unravelings
Bassi, Angelo; Ippoliti, Emiliano
2006-06-15
We analyze the geometric phase for an open quantum system when computed by resorting to a stochastic unraveling of the reduced density matrix (quantum jump approach or stochastic Schroedinger equations). We show that the resulting phase strongly depends on the type of unraveling used for the calculations: as such, this phase is not a geometric object since it depends on nonphysical parameters, which are not related to the path followed by the density matrix during the evolution of the system.
Information flow, non-Markovianity, and geometric phases
Wu, S. L.; Wang, L. C.; Yi, X. X.; Huang, X. L.
2010-11-15
Geometric phases and information flows of a two-level system coupled to its environment are calculated and analyzed. The information flow is defined as a cumulant of changes in trace distance between two quantum states, which is similar to the measure for non-Markovianity given by Breuer. We obtain an analytic relation between the geometric phase and the information flow for pure initial states, and a numerical result for mixed initial states. The geometric phase behaves differently depending on whether there are information flows back to the two-level system from its environment.
Voltage Controlled Geometric Phase Rotation in ^{208}Pb^{19}F.
NASA Astrophysics Data System (ADS)
Furneaux, J. E.; Shafer-Ray, Neil; Coker, J.; Rupasinghe, P. M.; McRaven, C. P.
2013-06-01
Many theoretical publications have investigated the impact of the geometric phase on measurements of the e-EDM. However, there has been surprisingly little quantitative comparison of these models with experiment. Here we create a quantum beat experiment that starts with an optical pump and ends with an optical probe of ^{208}Pb^{19}F. This measurement includes the ability to control a geometric phase variation of the molecular alignment by applying an appropriate bias voltage. These experiments will then used to test the accuracy of our model calculations of geometric phase rotation.
Geometric phase and its applications to fundamental physics
NASA Astrophysics Data System (ADS)
Capolupo, A.; Vitiello, G.
2016-09-01
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects, and thermal states. We show that the geometric phases appearing in the time evolution of mixed meson systems like Bs0- bar{{B}}_{{s}}^{{0}} and the K0- bar{{K}}^{{0}}_{} are linked to the parameter z describing the CPT violation. A non-zero phase difference between particle and antiparticle arises only in the presence of CPT symmetry breaking. Then the geometric phase can represent a completely new test for the CPT invariance. Moreover, we study the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution and propose the realization of interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature.
Non-adiabatic resonant conversion of solar neutrinos in three generations
NASA Astrophysics Data System (ADS)
Kim, C. W.; Nussinov, S.; Sze, W. K.
1987-02-01
The survival probability of solar electron neutrinos after non-adiabatic passage through the resonance-oscillation region in the Sun is discussed for the case of three generations. A method to calculate three-generation Landau-Zener transition probabilities between adiabatic states is described. We also discuss how the Landua-Zener probability is modified in the extreme non-adiabatic case.
Highly parallel implementation of non-adiabatic Ehrenfest molecular dynamics
NASA Astrophysics Data System (ADS)
Kanai, Yosuke; Schleife, Andre; Draeger, Erik; Anisimov, Victor; Correa, Alfredo
2014-03-01
While the adiabatic Born-Oppenheimer approximation tremendously lowers computational effort, many questions in modern physics, chemistry, and materials science require an explicit description of coupled non-adiabatic electron-ion dynamics. Electronic stopping, i.e. the energy transfer of a fast projectile atom to the electronic system of the target material, is a notorious example. We recently implemented real-time time-dependent density functional theory based on the plane-wave pseudopotential formalism in the Qbox/qb@ll codes. We demonstrate that explicit integration using a fourth-order Runge-Kutta scheme is very suitable for modern highly parallelized supercomputers. Applying the new implementation to systems with hundreds of atoms and thousands of electrons, we achieved excellent performance and scalability on a large number of nodes both on the BlueGene based ``Sequoia'' system at LLNL as well as the Cray architecture of ``Blue Waters'' at NCSA. As an example, we discuss our work on computing the electronic stopping power of aluminum and gold for hydrogen projectiles, showing an excellent agreement with experiment. These first-principles calculations allow us to gain important insight into the the fundamental physics of electronic stopping.
Non-Adiabatic MHD Modes in Periodic Magnetic Medium
NASA Astrophysics Data System (ADS)
Kumar, Nagendra; Kumar, Anil
High-resolution satellite observations reveal that many solar features such as penumbra and plume regions possess the structures with alternating properties. So we study the joint effect of periodic alternation of magnetic slabs and thermal mechanisms on the propagation of MHD waves. We consider a perfectly conducting fluid permeated by a magnetic field having the peri-odicity along x-axis and constant direction along z-axis. We suppose that the medium consists of alternating slabs of strong and weak homogeneous magnetic field with a sharp discontinuity at the boundary. The inclusion of non-adiabatic effects modifies the energy equation in which the thermal mechanisms (radiation, heating and thermal conduction) are added. The gravi-tational effects are negligible because wavelengths are assumed to be much smaller than the gravitational scale height. The dispersion relations for the surface and body modes are derived and analyzed in the limiting cases of thin and thick slabs. The dispersion curves depend upon the Bloch's wavenumber due to the periodicity in magnetic field. We have examined the be-havior of dispersion curves for different values of slab width ratio and Bloch's wavenumber as a function of dimensionless wavelength. It is shown that the width of structures influences the propagation speed of waves. Our results might be useful in understanding the wave propagation in plume regions, photosphere and spaghetti structures in solar wind.
NASA Astrophysics Data System (ADS)
Wu, Wei; Xu, Jing-Bo
2016-06-01
We investigate the quantum phase transition of an atomic ensemble trapped in a single-mode optical cavity via the geometric phase and quantum Fisher information of an extra probe atom which is injected into the optical cavity and interacts with the cavity field. We also find that the geometric quantum correlation between two probe atoms exhibits a double sudden transition phenomenon and show this double sudden transition phenomenon is closely associated with the quantum phase transition of the atomic ensemble. Furthermore, we propose a theoretical scheme to prolong the frozen time during which the geometric quantum correlation remains constant by applying time-dependent electromagnetic field.
Geometrical phase imprinted on eigenfunctions near an exceptional point
Lee, Soo-Young
2010-12-15
We illustrate how to get the geometric phase from eigenfunctions in the vicinity of an exceptional point in a dielectric microcavity whose non-Hermitian character comes from the outgoing-wave boundary condition. It is shown that the geometrical phase {+-}{pi} can be obtained either from total variation of the inner product of eigenfunctions or from a continuous change of phase plot, not of intensity plot, during a double cyclic parameter variation encircling the exceptional point. One can use either of the two ways by properly choosing the arbitrary phase of the calculated eigenfunctions.
Geometric phase in p -n junctions of helical edge states
NASA Astrophysics Data System (ADS)
Wadhawan, Disha; Mehta, Poonam; Das, Sourin
2016-02-01
The quantum spin Hall effect is endowed with topologically protected edge modes with a gapless Dirac spectrum. Applying a magnetic field locally along the edge leads to a gapped edge spectrum with the opposite parity for winding of spin texture for conduction and valence bands. Using Pancharatnam's prescription for the geometric phase it is shown that mismatch of this parity across a p -n junction, which could be engineered into the edge by electrical gate induced doping, leads to a phase dependence in the two-terminal conductance which is quantized to either zero or π . It is further shown that application of a nonuniform magnetic field across the junction could lead to a nonquantized value of this geometric phase which is tunable between zero and π . A current asymmetry measurement which is shown to be robust against electron-electron interactions is proposed to infer the appearance of this Pancharatnam's geometric phase in transport across such junctions.
Control of the spin geometric phase in semiconductor quantum rings
Nagasawa, Fumiya; Frustaglia, Diego; Saarikoski, Henri; Richter, Klaus; Nitta, Junsaku
2013-01-01
Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov–Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations. PMID:24067870
Geometric phases and cyclic isotropic cosmologies
NASA Astrophysics Data System (ADS)
Banchi, Leonardo; Caravelli, Francesco
2016-05-01
In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker Universe with a periodic scale factor, in which the Universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this Universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying the Berry phase of the scalar field, we show that contrary to what is commonly believed, the scalar field carries information from one bounce to another in the form of a global phase which occurs as generically non-zero. The Berry phase is then evaluated numerically in the case of the effective loop quantum cosmology closed Universe. We observe that Berry’s phase is non-zero, but that in the quantum regime the particle content is non-negligible.
Geometric Phase Appears in the Ultracold Hydrogen Exchange Reaction
NASA Astrophysics Data System (ADS)
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-10-01
Quantum reactive scattering calculations for the hydrogen exchange reaction H +H2 (v =4 ,j =0 )→H +H2 (v', j') and its isotopic analogues are reported for ultracold collision energies. Because of the unique properties associated with ultracold collisions, it is shown that the geometric phase effectively controls the reactivity. The rotationally resolved rate coefficients computed with and without the geometric phase are shown to differ by up to 4 orders of magnitude. The effect is also significant in the vibrationally resolved and total rate coefficients. The dynamical origin of the effect is discussed and the large geometric phase effect reported here might be exploited to control the reactivity through the application of external fields or by the selection of a particular nuclear spin state.
Optical Mode Control by Geometric Phase in Quasicrystal Metasurface
NASA Astrophysics Data System (ADS)
Yulevich, Igor; Maguid, Elhanan; Shitrit, Nir; Veksler, Dekel; Kleiner, Vladimir; Hasman, Erez
2015-11-01
We report on the observation of optical spin-controlled modes from a quasicrystalline metasurface as a result of an aperiodic geometric phase induced by anisotropic subwavelength structure. When geometric phase defects are introduced in the aperiodic structured surface, the modes exhibit polarization helicity dependence resulting in the optical spin-Hall effect. The radiative thermal dispersion bands from a quasicrystal structure are studied where the observed bands arise from the optical spin-orbit interaction induced by the aperiodic space-variant orientations of anisotropic antennas. The optical spin-flip behavior of the revealed modes that arise from the geometric phase pickup is experimentally observed within the visible spectrum by measuring the spin-projected diffraction patterns. The introduced ability to manipulate the light-matter interaction of quasicrystals in a spin-dependent manner provides the route for molding light via spin-optical aperiodic artificial planar surfaces.
Optical Mode Control by Geometric Phase in Quasicrystal Metasurface.
Yulevich, Igor; Maguid, Elhanan; Shitrit, Nir; Veksler, Dekel; Kleiner, Vladimir; Hasman, Erez
2015-11-13
We report on the observation of optical spin-controlled modes from a quasicrystalline metasurface as a result of an aperiodic geometric phase induced by anisotropic subwavelength structure. When geometric phase defects are introduced in the aperiodic structured surface, the modes exhibit polarization helicity dependence resulting in the optical spin-Hall effect. The radiative thermal dispersion bands from a quasicrystal structure are studied where the observed bands arise from the optical spin-orbit interaction induced by the aperiodic space-variant orientations of anisotropic antennas. The optical spin-flip behavior of the revealed modes that arise from the geometric phase pickup is experimentally observed within the visible spectrum by measuring the spin-projected diffraction patterns. The introduced ability to manipulate the light-matter interaction of quasicrystals in a spin-dependent manner provides the route for molding light via spin-optical aperiodic artificial planar surfaces. PMID:26613450
Geometric frustration phases of diblock copolymers in nanoparticles.
Li, Shiben; Chen, Peng; Zhang, Linxi; Liang, Haojun
2011-04-19
The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated. PMID:21417241
The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
NASA Astrophysics Data System (ADS)
Titum, Paraj; Berg, Erez; Rudner, Mark S.; Refael, Gil; Lindner, Netanel H.
Periodically driven quantum systems provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems; however, some of these phenomena are unique to the periodically driven case. Here, we show that disordered, periodically driven systems admit an ``anomalous'' two dimensional phase, whose quasi-energy spectrum consists of chiral edge modes that coexist with a fully localized bulk - an impossibility for static Hamiltonians. This unique situation serves as the basis for a new topologically-protected non-equilibrium transport phenomenon: quantized non-adiabatic charge pumping. We identify the bulk topological invariant that characterizes the new phase (which we call the ``anomalous Floquet Anderson Insulator'', or AFAI). We provide explicit models which constitute a proof of principle for the existence of the new phase. Finally, we present evidence that the disorder-driven transition from the AFAI to a trivial, fully localized phase is in the same universality class as the quantum Hall plateau transition.
Exploring percolative landscapes: Infinite cascades of geometric phase transitions
NASA Astrophysics Data System (ADS)
Timonin, P. N.; Chitov, Gennady Y.
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2 D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.
Exploring percolative landscapes: Infinite cascades of geometric phase transitions.
Timonin, P N; Chitov, Gennady Y
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters. PMID:26871019
Importance of Geometric Phase Effects in Ultracold Chemistry.
Hazra, Jisha; Kendrick, Brian K; Balakrishnan, Naduvalath
2015-12-17
It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scattering characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O2 reaction for total angular momentum quantum number J = 0-5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a "quantum switch" which can turn the reaction "on" or "off". PMID:26317912
Geometrical Series and Phase Space in a Finite Oscillatory Motion
ERIC Educational Resources Information Center
Mareco, H. R. Olmedo
2006-01-01
This article discusses some interesting physical properties of oscillatory motion of a particle on two joined inclined planes. The geometrical series demonstrates that the particle will oscillate during a finite time. Another detail is the converging path to the origin of the phase space. Due to its simplicity, this motion may be used as a…
Geometric phases, evolution loops and generalized oscillator potentials
NASA Technical Reports Server (NTRS)
Fernandez, David J.
1995-01-01
The geometric phases for dynamical processes where the evolution operator becomes the identity (evolution loops) are studied. The case of time-independent Hamiltonians with equally spaced energy levels is considered; special emphasis is made on the potentials having the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and their recently found coherent states.
A mechanical device to study geometric phases and curvatures
NASA Astrophysics Data System (ADS)
Gil, Salvador
2010-04-01
A simple mechanical device is introduced that can be used to illustrate the parallel transport of a vector along a curved surface and the geometric phase shift that occurs when a vector is carried along a loop on a curved surface. Its connection with the Foucault pendulum and Berry phases is discussed. The experimental results are in close agreement with the theoretical expectations. The experiment is inexpensive and conceptually easy to understand and perform.
Artefacts in geometric phase analysis of compound materials.
Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M
2015-10-01
The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. PMID:26094205
Molecular geometric phase from the exact electron-nuclear factorization
NASA Astrophysics Data System (ADS)
Requist, Ryan; Tandetzky, Falk; Gross, E. K. U.
2016-04-01
The Born-Oppenheimer electronic wave function ΦRBO(r ) picks up a topological phase factor ±1 , a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in R space. We show that this topological quantity reverts to a geometric quantity ei γ if the geometric phase γ =∮Im <ΦR|∇μΦR> .d Rμ is evaluated with the conditional electronic wave function ΦR(r ) from the exact electron-nuclear factorization ΦR(r ) χ (R ) instead of the adiabatic function ΦRBO(r ) . A model of a pseudorotating triatomic molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides examples of nontrivial induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current that cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wave function.
Nonlinearity of Pancharatnam's geometric phase in polarizing interferometers.
Hils, B; Dultz, W; Martienssen, W
1999-08-01
Earlier investigations show a time-variable nonlinear shift of the fringe pattern in a polarizing interferometer while rotating a polarizer at the exit. This effect was identified as Pancharatnam's geometrical phase and proposed for applications in interferometry and fast optical switching devices. A heterodyne analysis attributes moving fringes to a frequency difference between the interfering beams; thus changing fringe velocities point to a dynamic frequency development within the period of the uniformly rotating analyzer. This explanation offends the intuition and we undertake an experimental and theoretical investigation of the effect to solve the paradox. We determine, e.g., the complete frequency and mode spectrum of an arbitrary state of polarization P0 behind a rotating linear analyzer and behind a rotating arbitrary linear birefringent plate. We find that, in spite of a fast changing phase in the interferometer, no other (higher) frequency components appear in the spectral distribution of the intensity at the exit than the double of the rotary frequency of the analyzer: phase nonlinearities are compensated for by intensity changes. Only a phase-sensitive detector like an array of photodetectors is able to observe the nonlinearity of Pancharatnam's geometrical phase. A single detector only finds a sinusoidal intensity variation. Our insight into these relations leads us to two new applications of Pancharatnam's phase: supersensitivity of a polarizing double beam interferometer with a video camera acting as a phase detector and external tuning of a Fizeau interferometer. PMID:11970029
Non-adiabatic holonomic quantum computation in linear system-bath coupling
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-01-01
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities. PMID:26846444
Non-adiabatic holonomic quantum computation in linear system-bath coupling
NASA Astrophysics Data System (ADS)
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-02-01
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
Geometric phase in Stückelberg interferometry
NASA Astrophysics Data System (ADS)
Lim, Lih-King; Fuchs, Jean-Noël; Montambaux, Gilles
2015-04-01
We study the time evolution of a two-dimensional quantum particle exhibiting a two-band energy spectrum with two Dirac cones as, for example, in the honeycomb lattice. A force is applied such that the particle experiences two Landau-Zener transitions in succession in the vicinity of the Dirac cones. The adiabatic evolution between the two transitions leads to Stückelberg interferences, due to two possible trajectories in energy-momentum space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign associated with each Dirac cone, as well as on the type of trajectory (parallel or diagonal with respect to the two cones) in parameter space. This geometric phase reveals the coupling between the bands encoded in the structure of the wave functions. Stückelberg interferometry therefore appears as a way to access both intra- and interband geometric information.
Some geometric properties of quantum phases and calculation of phase formulas
NASA Astrophysics Data System (ADS)
Bracken, Paul
An introduction to several geometrical ideas which are of use to quantum mechanics is presented. The Aharonov-Anandan phase is introduced and without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fiber bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure.
Geometric phases of the Faraday rotation of electromagnetic waves in magnetized plasmas
Liu Jian; Qin Hong
2012-10-15
Geometric phases of circularly polarized electromagnetic waves in nonuniform magnetized plasmas is studied theoretically. The variation of the propagation direction of circularly polarized waves results in a geometric phase, which also contributes to the Faraday rotation, in addition to the standard dynamical phase. The origin and properties of the geometric phase are investigated. The influence of the geometric phase to plasma diagnostics using the Faraday rotation is discussed as an application of the theory.
Geometric Phase Of The Faraday Rotation Of Electromagnetic Waves In Magnetized Plasma
Jian Liu and Hong Qin
2011-11-07
The geometric phase of circularly polarized electromagnetic waves in nonuniform magnetized plasmas is studied theoretically. The variation of the propagation direction of circularly polarized waves results in a geometric phase, which also contributes to the Faraday rotation, in addition to the standard dynamical phase. The origin and properties of the geometric phase is investigated. The in uence of the geometric phase to plasma diagnostics using Faraday rotation is also discussed as an application of the theory.
Non Abelian structures and the geometric phase of entangled qudits
Oxman, L.E. Khoury, A.Z.
2014-12-15
In this work, we address some important topological and algebraic aspects of two-qudit states evolving under local unitary operations. The projective invariant subspaces and evolutions are connected with the common elements characterizing the su(d) Lie algebra and their representations. In particular, the roots and weights turn out to be natural quantities to parametrize cyclic evolutions and fractional phases. This framework is then used to recast the coset contribution to the geometric phase in a form that generalizes the usual monopole-like formula for a single qubit.
Geometric phases causing lifetime modifications of metastable states of hydrogen
NASA Astrophysics Data System (ADS)
Trappe, Martin-Isbjörn; Augenstein, Peter; DeKieviet, Maarten; Gasenzer, Thomas; Nachtmann, Otto
2016-04-01
Externally applied electromagnetic fields in general have an influence on the width of atomic spectral lines. The decay rates of atomic states can also be affected by the geometry of an applied field configuration giving rise to an imaginary geometric phase. A specific chiral electromagnetic field configuration is presented which geometrically modifies the lifetimes of metastable states of hydrogen. We propose to extract the relevant observables in a realistic longitudinal atomic beam spin-echo apparatus which allows the initial and final fluxes of the metastable atoms to be compared with each other interferometrically. A geometry-induced change in lifetimes at the 5%-level is found, an effect large enough to be observed in an available experiment.
Measuring the Aharonov–Anandan phase in multiport photonic systems
NASA Astrophysics Data System (ADS)
Wang, Kai; Weimann, Steffen; Nolte, Stefan; Perez-Leija, Armando; Szameit, Alexander
2016-04-01
The Aharonov-Anandan phase is a description of the geometric nature in non-adiabatic cyclic evolutions of quantum states. Here we report on a measurement of the Aharonov-Anandan phase in photonics. We consider a time-independent quantum driven harmonic oscillator that is initially prepared at the vacuum state. We utilize evanescently coupled waveguides to realize this physical model and achieve a measurement of the Aharonov-Anandan phase via integrated interferometry.
NASA Astrophysics Data System (ADS)
Dupret, M.-A.; De Ridder, J.; De Cat, P.; Aerts, C.; Scuflaire, R.; Noels, A.; Thoul, A.
2003-02-01
We present an improved version of the method of photometric mode identification of Heynderickx et al. (\\cite{hey}). Our new version is based on the inclusion of precise non-adiabatic eigenfunctions determined in the outer stellar atmosphere according to the formalism recently proposed by Dupret et al. (\\cite{dup}). Our improved photometric mode identification technique is therefore no longer dependent on ad hoc parameters for the non-adiabatic effects. It contains the complete physical conditions of the outer atmosphere of the star, provided that rotation does not play a key role. We apply our method to the two slowly pulsating B stars HD 74560 and HD 138764 and to the beta Cephei star EN (16) Lac. Besides identifying the degree l of the pulsating stars, our method is also a tool for improving the knowledge of stellar interiors and atmospheres, by imposing constraints on parameters such as the metallicity and the mixing-length parameter alpha (a procedure we label non-adiabatic asteroseismology). The non-adiabatic eigenfunctions needed for the mode identification are available upon request from the authors.
Non-adiabatic spin-transfer torque independent of the spin relaxation rate
NASA Astrophysics Data System (ADS)
Kim, Kyoung-Whan; Lee, Kyung-Jin; Lee, Hyun-Woo; Stiles, Mark
Non-adiabatic spin-transfer torques play an important role in magnetization dynamics. For example, they determine current-induced magnetic domain wall velocity. A well-known mechanism for non-adiabatic spin-transfer torques arises from spin relaxation and is directly proportional to the spin relaxation rate. Here we report mechanism that is independent of the spin relaxation rate. This mechanism is related to the recently reported intrinsic damping-like spin-orbit torque, which is proportional to an electric field but is independent of the conductivity, and hence the scattering rate. Likewise, the mechanism we report is independent of the scattering rate. It originates from the effective spin-orbit coupling that arises in systems with magnetic textures as we previously reported for related processes. In this work, we demonstrate the existence of such a spin-transfer torque, which is a contribution to the non-adiabatic spin-transfer torque and is independent of scattering rates. We also demonstrate that the magnitude of this torque can be much larger than other mechanisms for non-adiabatic spin-transfer torques, and may be the dominant contribution in some systems.
A study of geometric phase topology using Fourier transform method
NASA Astrophysics Data System (ADS)
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-07-01
Topological aspect of the geometric phase (GP) due to pure polarization projection is studied using the 2D Fourier transform (2D-FT) method. Projection of orthogonal polarization state results in a phase singularity in the 2D parameter space of ellipticity and orientation of polarization ellipse. Projection of its surrounding states results in an accumulation of GP in different amount that form a spiral structure. A half wave plate–quarter wave plate combination is used to generate different polarization states which are projected using a polarizer. The accumulated phase for each orientation of the wave plate is extracted from 2D-FT of the interferogram, obtained by interfering it with a reference beam in a Mach–Zehnder like interferometer.
Geometric phase and gauge connection in polyatomic molecules.
Wittig, Curt
2012-05-14
Geometric phase is an interesting topic that is germane to numerous and varied research areas: molecules, optics, quantum computing, quantum Hall effect, graphene, and so on. It exists only when the system of interest interacts with something it perceives as exterior. An isolated system cannot display geometric phase. This article addresses geometric phase in polyatomic molecules from a gauge field theory perspective. Gauge field theory was introduced in electrodynamics by Fock and examined assiduously by Weyl. It yields the gauge field A(μ), particle-field couplings, and the Aharonov-Bohm phase, while Yang-Mills theory, the cornerstone of the standard model of physics, is a template for non-Abelian gauge symmetries. Electronic structure theory, including nonadiabaticity, is a non-Abelian gauge field theory with matrix-valued covariant derivative. Because the wave function of an isolated molecule must be single-valued, its global U(1) symmetry cannot be gauged, i.e., products of nuclear and electron functions such as χ(n)ψ(n) are forbidden from undergoing local phase transformation on R, where R denotes nuclear degrees of freedom. On the other hand, the synchronous transformations (first noted by Mead and Truhlar): ψ(n)→ψ(n)e(iζ) and simultaneously χ(n)→χ(n)e(-iζ), preserve single-valuedness and enable wave functions in each subspace to undergo phase transformation on R. Thus, each subspace is compatible with a U(1) gauge field theory. The central mathematical object is Berry's adiabatic connection i
Geometrically-frustrated pseudogap phase of Coulomb liquids
NASA Astrophysics Data System (ADS)
Pramudya, Y.; Terletska, H.; Pankov, S.; Manousakis, E.; Dobrosavljević, V.
2012-06-01
We study a class of models with long-range repulsive interactions of the generalized Coulomb form V(r)∼1/rα. We show that decreasing the interaction exponent in the regime α
Martínez-Mesa, Aliezer; Saalfrank, Peter
2015-05-21
Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the “curse of dimensionality” encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influence of the different parameters determining the shape of a laser pulse (e.g., its finite width and a possible chirp) on the predissociation dynamics of a NaI molecule, upon photoexcitation of the A(0{sup +}) state. The finite-pulse effects are mapped into the initial conditions for semiclassical surface-hopping simulations. The simulated surface-hopping diabatic populations are in qualitative agreement with the quantum mechanical results, especially concerning the subpicosend photoinduced dynamics, the main deviations being the relative delay of the non-adiabatic transitions in the semiclassical picture. Likewise, these differences in the time-dependent electronic populations calculated via the semiclassical and the quantum methods are found to have a mild influence on the overall probability density distribution. As a result, the branching ratios between the bound and the dissociative reaction channels and the time-evolution of the molecular wavepacket predicted by the semiclassical method agree with those computed using quantum wavepacket propagation. Implications for more challenging molecular systems are given.
Classification theorem for principal fibre bundles, Berry's phase, and exact cycle evolution
Bohm, A.; Boya, L.J.; Mostafazadeh, A. . Center for Particle Physics); Rudolph, G. . Fachbereich Physik)
1993-03-01
The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors.
Classification theorem for principal fibre bundles, Berry`s phase, and exact cycle evolution
Bohm, A.; Boya, L.J.; Mostafazadeh, A.; Rudolph, G.
1993-03-01
The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors.
Geometric phase-shifting for low-coherence interference microscopy
NASA Astrophysics Data System (ADS)
Roy, M.; Svahn, P.; Cherel, L.; Sheppard, C. J. R.
2002-06-01
A low-coherence Linnik interference microscope using high numerical aperture optics has been constructed. The system uses a tungsten halogen lamp and Köhler illumination, with separate control over field and aperture stops, so that experiments can be conducted with a range of different operating conditions. The novel feature of the system is the use of an achromatic phase-shifter operating on the principle of the geometric phase, achieved by using a polarising beam splitter, a quarter wave plate and a rotating polariser. Image information is extracted from the visibility of the fringes, the position of the visibility peak along the scanning axis yielding the height of the test surface at the corresponding point.
Ultrafast hydrogen migration in acetylene cation driven by non-adiabatic effects.
Madjet, Mohamed El-Amine; Li, Zheng; Vendrell, Oriol
2013-03-01
Non-adiabatic dynamics of the acetylene cation is investigated using mixed quantum-classical dynamics based on trajectory surface hopping. To describe the non-adiabatic effects, two surface hopping methods are used, namely, Tully's fewest switches and Landau-Zener surface hopping. Similarities and differences between the results based on those two methods are discussed. We find that the photoionization of acetylene into the first excited state A(2)Σg(+) drives the molecule from the linear structure to a trans-bent structure. Through a conical intersection the acetylene cation can relax back to either the ground state of acetylene or vinylidene. We conclude that hydrogen migration always takes place after non-radiative electronic relaxation to the ground state of the monocation. Based on the analysis of correlation functions we identify coherent oscillations between acetylene and vinylidene with a period of about 70 fs after the electronic relaxation. PMID:23485298
Non-adiabatic dynamics close to conical intersections and the surface hopping perspective.
Malhado, João Pedro; Bearpark, Michael J; Hynes, James T
2014-01-01
Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field. PMID:25485263
Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces
NASA Astrophysics Data System (ADS)
Hu, Shi; Cui, Wen-Xue; Guo, Qi; Wang, Hong-Fu; Zhu, Ai-Dong; Zhang, Shou
2016-06-01
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here, we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented by utilizing non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.
Determination of the spin torque non-adiabaticity in perpendicularly magnetized nanowires.
Heinen, J; Hinzke, D; Boulle, O; Malinowski, G; Swagten, H J M; Koopmans, B; Ulysse, C; Faini, G; Ocker, B; Wrona, J; Kläui, M
2012-01-18
Novel nanofabrication methods and the discovery of an efficient manipulation of local magnetization based on spin polarized currents has generated a tremendous interest in the field of spintronics. The search for materials allowing for fast domain wall dynamics requires fundamental research into the effects involved (Oersted fields, adiabatic and non-adiabatic spin torque, Joule heating) and possibilities for a quantitative comparison. Theoretical descriptions reveal a material and geometry dependence of the non-adiabaticity factor β, which governs the domain wall velocity. Here, we present two independent approaches for determining β: (i) measuring the dependence of the dwell times for which a domain wall stays in a metastable pinning state on the injected current and (ii) the current-field equivalence approach. The comparison of the deduced β values highlights the problems of using one-dimensional models to describe two-dimensional dynamics and allows us to ascertain the reliability, robustness and limits of the approaches used. PMID:22172802
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation
NASA Astrophysics Data System (ADS)
Zamstein, Noa; Tannor, David J.
2012-12-01
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)], 10.1063/1.2400851 to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)], 10.1063/1.459170. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.
NASA Astrophysics Data System (ADS)
Hofmann, C.; Zimmermann, T.; Zielinski, A.; Landsman, A. S.
2016-04-01
The validity of the adiabatic approximation in strong field ionization under typical experimental conditions has recently become a topic of great interest. Experimental results have been inconclusive, in part, due to the uncertainty in experimental calibration of intensity. Here we turn to the time-dependent Schrödinger equation, where all the laser parameters are known exactly. We find that the centre of the electron momentum distribution (typically used for calibration of elliptically and circularly polarized light) is sensitive to non-adiabatic effects, leading to intensity shifts in experimental data that can significantly affect the interpretation of results. On the other hand, the transverse momentum spread in the plane of polarization is relatively insensitive to such effects, even in the Keldysh parameter regime approaching γ ≈ 3. This suggests the transverse momentum spread in the plane of polarization as a good alternative to the usual calibration method, particularly for experimental investigation of non-adiabatic effects using circularly polarized light.
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.
Zamstein, Noa; Tannor, David J
2012-12-14
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations. PMID:23249054
Non-adiabatic dynamics close to conical intersections and the surface hopping perspective
Malhado, João Pedro; Bearpark, Michael J.; Hynes, James T.
2014-01-01
Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field. PMID:25485263
Quantum and classical non-adiabatic dynamics of Li_{2}^{+}Ne photodissociation
NASA Astrophysics Data System (ADS)
Pouilly, Brigitte; Monnerville, Maurice; Zanuttini, David; Gervais, Benoît
2015-01-01
The 3D photodissociation dynamics of Li2+Ne system is investigated by quantum calculations using the multi-configuration time-dependent Hartree (MCTDH) method and by classical simulations with the trajectory surface hopping (TSH) approach. Six electronic states of A’ symmetry and two states of A” symmetry are involved in the process. Couplings in the excitation region and two conical intersections in the vicinity of the Franck-Condon zone control the non-adiabatic nuclear dynamics. A diabatic representation including all the states and the couplings is determined. Diabatic and adiabatic populations calculated for initial excitation to pure diabatic and adiabatic states lead to a clear understanding of the mechanisms governing the non-adiabatic photodissociation process. The classical and quantum photodissociation cross-sections for absorption in two adiabatic states of the A’ symmetry are calculated. A remarkable agreement between quantum and classical results is obtained regarding the populations and the absorption cross-sections.
Non-adiabatic response of relativistic radiation belt electrons to GEM magnetic storms
NASA Astrophysics Data System (ADS)
McAdams, K. L.; Reeves, G. D.
The importance of fully adiabatic effects in the relativistic radiation belt electron response to magnetic storms is poorly characterized due to many difficulties in calculating adiabatic flux response. Using the adiabatic flux model of Kim and Chan [1997a] and Los Alamos National Laboratory geosynchronous satellite data, we examine the relative timing of the adiabatic and non-adiabatic flux responses. In the three storms identified by the GEM community for in depth study, the non-adiabatic energization occurs hours earlier than the adiabatic re-energization. The adiabatic energization can account for only 10-20% of the flux increases in the first recovery stages, and only 1% of the flux increase if there is continuing activity.
Coverage dependent non-adiabaticity of CO on a copper surface
Omiya, Takuma; Arnolds, Heike
2014-12-07
We have studied the coverage-dependent energy transfer dynamics between hot electrons and CO on Cu(110) with femtosecond visible pump, sum frequency probe spectroscopy. We find that transients of the C–O stretch frequency display a red shift, which increases from 3 cm{sup −1} at 0.1 ML to 9 cm{sup −1} at 0.77 ML. Analysis of the transients reveals that the non-adiabatic coupling between the adsorbate vibrational motion and the electrons becomes stronger with increasing coverage. This trend requires the frustrated rotational mode to be the cause of the non-adiabatic behavior, even for relatively weak laser excitation of the adsorbate. We attribute the coverage dependence to both an increase in the adsorbate electronic density of states and an increasingly anharmonic potential energy surface caused by repulsive interactions between neighboring CO adsorbates. This work thus reveals adsorbate-adsorbate interactions as a new way to control adsorbate non-adiabaticity.
Adiabatic geometric phase for a Bose-Einstein condensate coupled to a cavity
Li Shengchang; Fu Libin; Liu Jie
2011-11-15
We investigate the geometric phase in a model of a Bose-Einstein condensate coupled to an optical cavity in which both the condensate and the cavity are described with coherent states. When the argument of the atom-cavity coupling term varies in time slowly from zero to 2{pi}, we calculate the geometric phase accumulated by the ground state and obtain its analytic expression in explicit form. We find that the adiabatic geometric phase jumps from zero to nontrivial {pi} at a critical value that corresponds to the normal-superradiant phase-transition point. The magneticlike flux interpretation of the geometric phase is also discussed.
Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics
Berrada, K.
2014-01-15
Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution. -- Highlights: •Geometric phase under noise phase laser. •Dynamics of the geometric phase under non-Markovian dynamics in the presence of classical noise. •Solution of master equation of the system in terms atomic inversion. •Nonlocal correlation between the system and its environment under non-Markovianity.
Geometric phase of mixed states for three-level open systems
Jiang Yanyan; Ji, Y. H.; Wang, Z. S.; Xu Hualan; Hu Liyun; Chen, Z. Q.; Guo, L. P.
2010-12-15
Geometric phase of mixed state for three-level open system is defined by establishing in connecting density matrix with nonunit vector ray in a three-dimensional complex Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. Under the limiting of pure state, our approach is in agreement with the Berry phase, Pantcharatnam phase, and Aharonov and Anandan phase. We find that, furthermore, the Berry phase of mixed state correlated to population inversions of three-level open system.
Multiple coupled landscapes and non-adiabatic dynamics with applications to self-activating genes.
Chen, Cong; Zhang, Kun; Feng, Haidong; Sasai, Masaki; Wang, Jin
2015-11-21
Many physical, chemical and biochemical systems (e.g. electronic dynamics and gene regulatory networks) are governed by continuous stochastic processes (e.g. electron dynamics on a particular electronic energy surface and protein (gene product) synthesis) coupled with discrete processes (e.g. hopping among different electronic energy surfaces and on and off switching of genes). One can also think of the underlying dynamics as the continuous motion on a particular landscape and discrete hoppings among different landscapes. The main difference of such systems from the intra-landscape dynamics alone is the emergence of the timescale involved in transitions among different landscapes in addition to the timescale involved in a particular landscape. The adiabatic limit when inter-landscape hoppings are fast compared to continuous intra-landscape dynamics has been studied both analytically and numerically, but the analytical treatment of the non-adiabatic regime where the inter-landscape hoppings are slow or comparable to continuous intra-landscape dynamics remains challenging. In this study, we show that there exists mathematical mapping of the dynamics on 2(N) discretely coupled N continuous dimensional landscapes onto one single landscape in 2N dimensional extended continuous space. On this 2N dimensional landscape, eddy current emerges as a sign of non-equilibrium non-adiabatic dynamics and plays an important role in system evolution. Many interesting physical effects such as the enhancement of fluctuations, irreversibility, dissipation and optimal kinetics emerge due to non-adiabaticity manifested by the eddy current illustrated for an N = 1 self-activator. We further generalize our theory to the N-gene network with multiple binding sites and multiple synthesis rates for discretely coupled non-equilibrium stochastic physical and biological systems. PMID:26455835
Non-adiabatic effects on the optical response of driven systems
NASA Astrophysics Data System (ADS)
Fregoso, Benjamin M.; Kolodrubetz, Michael; Moore, Joel
Periodically driven systems have received renewed interest due to their capacity to engineer non-trivial effective Hamiltonians. A characteristic of such systems is how they respond to weak periodicity-breaking drive, as for example when a laser is pulsed instead of continuous wave. We develop semi-classical equations of motion of a wave packet in the presence of electric and magnetic fields which are turned on non-adiabatically. We then show the emergence of significant corrections to electronic collective excitations and optical responses of topological insulator surface states, Weyl metals and semiconductor mono-chalcogenides.
The molecular symmetry adapted non - adiabatic coupling terms and diabatic Hamiltonian matrix
NASA Astrophysics Data System (ADS)
Mukherjee, Saikat; Bandyopadhyay, Sudip; Paul, Amit Kumar; Adhikari, Satrajit
2013-04-01
We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non - Adiabatic Coupling Terms (NACTs) for the excited electronic states (22 E' and 12 A'1) of Na3 cluster at the MRCI level by using ab initio quantum chemistry package (MOLPRO), where the NACTs are adapted with Molecular Symmetry (MS) by employing appropriate Irreducible Representations (IREPs). Such terms are incorporated into the Adiabatic to Diabatic Transformation (ADT) equations to obtain the ADT angles to construct the continuous, single - valued, symmetric and smooth 3 × 3 diabatic Hamiltonian matrix.
A dynamical approach to non-adiabatic electron transfers at the bio-inorganic interface.
Zanetti-Polzi, Laura; Corni, Stefano
2016-04-21
A methodology is proposed to investigate electron transfer reactions between redox-active biomolecular systems (e.g. a protein) and inorganic surfaces. The whole system is modelled at the atomistic level using classical molecular dynamics - making an extensive sampling of the system's configurations possible - and the energies associated with the redox-active complex reduction are calculated using a hybrid quantum/classical approach along the molecular dynamics trajectory. The non-adiabaticity is introduced a posteriori using a Monte Carlo approach based on the Landau-Zener theory extended to treat a metal surface. This approach thus allows us to investigate the role of the energy fluctuations, determined by the dynamical evolution of the system, as well as the role of non-adiabaticity in affecting the kinetic rate of the electron transfer reaction. Most notably, it allows us to investigate the two contributions separately, hence achieving a detailed picture of the mechanisms that determine the rate. The analysis of the system configurations also allows us to relate the estimated electronic coupling to the structural and dynamic properties of the system. As a test case, the methodology is here applied to study the electron transfer reaction between cytochrome c and a gold surface. The results obtained explain the different electron transfer rates experimentally measured for two different concentrations of proteins on the electrode surface. PMID:27031179
NASA Astrophysics Data System (ADS)
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T.; Gross, E. K. U.
2015-03-01
The Born-Oppenheimer (BO) approximation allows to visualize the coupled electron-nuclear dynamics in molecular systems as a set of nuclei moving on a single potential energy surface representing the effect of the electrons in a given eigenstate. Many interesting phenomena, however, such as vision or charge separation in organic photovoltaic materials, take place in conditions beyond its range of validity. Nevertheless, the basic construct of the adiabatic treatment, the BO potential energy surfaces, is employed to describe non-adiabatic processes and the full problem is represented in terms of adiabatic states and transitions among them in regions of strong non-adiabatic coupling. But the concept of single potential energy is lost. The alternative point of view arising in the framework of the exact factorization of the electron-nuclear wave function will be presented. A single, time-dependent, potential energy provides the force driving the nuclear motion and is adopted as starting point for the development of quantum-classical approximations to the full quantum mechanical problem.
Taple-top imaging of the non-adiabatically driven isomerization in the acetylene cation
NASA Astrophysics Data System (ADS)
Beaulieu, Samuel; Ibrahim, Heide; Wales, Benji; Schmidt, Bruno E.; Thiré, Nicolas; Bisson, Éric; Hebeisen, Christoph T.; Wanie, Vincent; Giguere, Mathieu; Kieffer, Jean-Claude; Sanderson, Joe; Schuurman, Michael S.; Légaré, François
2014-05-01
One of the primary goals of modern ultrafast science is to follow nuclear and electronic evolution of molecules as they undergo a photo-chemical reaction. Most of the interesting dynamics phenomena in molecules occur when an electronically excited state is populated. When the energy difference between electronic ground and excited states is large, Free Electron Laser (FEL) and HHG-based VUV sources were, up to date, the only light sources able to efficiently initiate those non-adiabatic dynamics. We have developed a simple table-top approach to initiate those rich dynamics via multiphoton absorption. As a proof of principle, we studied the ultrafast isomerization of the acetylene cation. We have chosen this model system for isomerization since the internal conversion mechanism which leads to proton migration is still under debate since decades. Using 266 nm multiphoton absorption as a pump and 800 nm induced Coulomb Explosion as a probe, we have shoot the first high-resolution molecular movie of the non-adiabatically driven proton migration in the acetylene cation. The experimental results are in excellent agreement with high level ab initio trajectory simulations.
Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit
Mohamed, A.-B.A.; Obada, A.-S.F.
2011-09-15
Analytical descriptions of the geometric phases (GPs) for the total system and subsystems are studied for a current biased Josephson phase qubit strongly coupled to a lossy LC circuit in the dispersive limit. It is found that, the GP and purity depend on the damping parameter which leads to the phenomenon of GP death. Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP. The asymptotic behavior of the GP and the purity for the qubit-LC resonator state closely follow that for the qubit state, but however, for the LC circuit these asymptotic values are equal to zero. - Highlights: > The model of a current biased Josephson phase qubit, strongly coupled to loss LC circuit, is considered. > Analytical descriptions of the geometric phase (GP) of this model, in the dispersive limit, are studied. > The GP and purity depend on the dissipation which leads to the GP death phenomenon. > Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP.
Non-Abelian geometric phase and long-range atomic forces
NASA Technical Reports Server (NTRS)
Zygelman, B.
1990-01-01
It is shown how gauge fields, or geometric phases, manifest as observable effects in both bound and free diatom systems. It is shown that, in addition to altering energy splittings in bound systems, geometric phases induce transitions in levels separated by a finite-energy gap. An example is given where the non-Abelian gauge field couples nondegenerate electronic levels in a diatom. This gauge-field coupling gives rise to an observable effect. It is shown that when the diatom is 'pulled apart', the non-Abelian geometric phase manifests as a long-range atomic force.
Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media
NASA Astrophysics Data System (ADS)
Rafayelyan, Mushegh; Tkachenko, Georgiy; Brasselet, Etienne
2016-06-01
We report on highly reflective spin-orbit geometric phase optical elements based on a helicity-preserving circular Bragg-reflection phenomenon. First, we present a dynamical geometric phase experiment using a flat chiral Bragg mirror. Then, we show that shaping such a geometric phase allows the efficient spin-orbit tailoring of light fields without the need to fulfill any condition on birefringent phase retardation, in contrast to the case of transmission spin-orbit optical elements. This is illustrated by optical vortex generation from chiral liquid crystal droplets in the Bragg regime that unveils spin-orbit consequences of the droplet's curvature. Our results thus introduce a novel class of geometric phase elements—"Bragg-Berry" optical elements.
Non-adiabatic molecular dynamic simulations of opening reaction of molecular junctions
NASA Astrophysics Data System (ADS)
Zobač, Vladmír; Lewis, James P.; Jelínek, Pavel
2016-07-01
We report non-adiabatic molecular dynamic simulations of the ring opening reaction of diarylethene (DAE) derivative molecules, both free standing and embedded between gold electrodes. Simulations are performed by the surface hopping method employing density functional theory. Typically, the free-standing molecules exhibit large quantum yields to open and close; however the process is quenched for the molecules embedded between electrodes. Our simulations reveal the importance of the DAE side chemical groups, which explain the efficiency of the quenching process. Namely, delocalization of the LUMO state contributes to electronic coupling between the molecule and electrodes, suppressing or enhancing the reaction process. The simulations indicate that a proper choice of the chemical side group, which provides the strong localization of the LUMO state, can substantially diminish the quenching mechanism. Additionally, we analyze a strong dependency of the quantum yield of the opening reaction coming from the mechanical strength of the molecules.
Non-adiabatic molecular dynamic simulations of opening reaction of molecular junctions.
Zobač, Vladmír; Lewis, James P; Jelínek, Pavel
2016-07-15
We report non-adiabatic molecular dynamic simulations of the ring opening reaction of diarylethene (DAE) derivative molecules, both free standing and embedded between gold electrodes. Simulations are performed by the surface hopping method employing density functional theory. Typically, the free-standing molecules exhibit large quantum yields to open and close; however the process is quenched for the molecules embedded between electrodes. Our simulations reveal the importance of the DAE side chemical groups, which explain the efficiency of the quenching process. Namely, delocalization of the LUMO state contributes to electronic coupling between the molecule and electrodes, suppressing or enhancing the reaction process. The simulations indicate that a proper choice of the chemical side group, which provides the strong localization of the LUMO state, can substantially diminish the quenching mechanism. Additionally, we analyze a strong dependency of the quantum yield of the opening reaction coming from the mechanical strength of the molecules. PMID:27255903
The exact forces on classical nuclei in non-adiabatic charge transfer.
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T; Gross, E K U
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect. PMID:25725727
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
NASA Astrophysics Data System (ADS)
Zamstein, Noa; Tannor, David J.
2012-12-01
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schrödinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)], 10.1063/1.4739845. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], 10.1063/1.459170, and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
Fernandez-Alberti, Sebastian; Makhov, Dmitry V; Tretiak, Sergei; Shalashilin, Dmitrii V
2016-04-21
Photoinduced dynamics of electronic and vibrational unidirectional energy transfer between meta-linked building blocks in a phenylene ethynylene dendrimer is simulated using a multiconfigurational Ehrenfest in time-dependent diabatic basis (MCE-TDDB) method, a new variant of the MCE approach developed by us for dynamics involving multiple electronic states with numerous abrupt crossings. Excited-state energies, gradients and non-adiabatic coupling terms needed for dynamics simulation are calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. A comparative analysis of our results obtained using MCE-TDDB, the conventional Ehrenfest method and the surface-hopping approach with and without decoherence corrections is presented. PMID:27004611
Investigation of spontaneous Brillouin scattering generation based on non-adiabatic microfibres
NASA Astrophysics Data System (ADS)
Zarei, A.; Jasim, A. A.; Harun, S. W.; Ahmad, H.
2014-12-01
Brillouin Stokes and anti-Stokes generation is successfully demonstrated in backward direction using a non-adiabatic microfibre as the gain medium. The Stokes light wavelength is up-shifted by 0.088 nm (10 GHz) from the BP wavelength as monitored by using an optical spectrum analyzer. The Brillouin scattering can also be enhanced by employing a microfibre based inline Mach-Zehnder interferometer (IMZI) as the gain medium due to its stronger multimode interference effect. It is shown that the microfibre geometry plays an important role in the spontaneous Brillouin scattering generation and gain bandwidth broadening due to its effect on irritation of the acoustic modes inside the microfibre.
Non-adiabatic generation of NOON states in a Tonks-Girardeau gas
NASA Astrophysics Data System (ADS)
Schloss, James; Benseny, Albert; Gillet, Jérémie; Swain, Jacob; Busch, Thomas
2016-03-01
Adiabatic techniques can be used to control quantum states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may be isolated from the environment only for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity can be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks-Girardeau gases. Dedicated to the memory of Marvin D Girardeau.
Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes
NASA Astrophysics Data System (ADS)
Agostini, Federica; Min, Seung Kyu; Gross, E. K. U.
2015-10-01
In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schroedinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics.
The exact forces on classical nuclei in non-adiabatic charge transfer
NASA Astrophysics Data System (ADS)
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T.; Gross, E. K. U.
2015-02-01
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
The exact forces on classical nuclei in non-adiabatic charge transfer
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Gross, E. K. U.; Maitra, Neepa T.
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
Zamstein, Noa; Tannor, David J.
2012-12-14
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schroedinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
Gidopoulos, Nikitas I.; Gross, E. K. U.
2014-01-01
A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born–Oppenheimer (BO)-type product of a nuclear wave function, X(R), and an electronic one, ΦR(r), which depends parametrically on the nuclear configuration R. From the variational principle, we deduce formally exact equations for ΦR(r) and X(R). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron–nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential. PMID:24516183
Inflationary perturbation theory is geometrical optics in phase space
NASA Astrophysics Data System (ADS)
Seery, David; Mulryne, David J.; Frazer, Jonathan; Ribeiro, Raquel H.
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "δN" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
Inflationary perturbation theory is geometrical optics in phase space
Seery, David; Frazer, Jonathan; Mulryne, David J.; Ribeiro, Raquel H. E-mail: D.Mulryne@qmul.ac.uk E-mail: R.Ribeiro@damtp.cam.ac.uk
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ({sup t}ransport equations{sup )}, analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar 'δN' Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of f{sub NL} in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
Geometric Phase of the Gyromotion for Charged Particles in a Time-dependent Magnetic Field
Jian Liu and Hong Qin
2011-07-18
We study the dynamics of the gyrophase of a charged particle in a magnetic field which is uniform in space but changes slowly with time. As the magnetic field evolves slowly with time, the changing of the gyrophase is composed of two parts. The rst part is the dynamical phase, which is the time integral of the instantaneous gyrofrequency. The second part, called geometric gyrophase, is more interesting, and it is an example of the geometric phase which has found many important applications in different branches of physics. If the magnetic field returns to the initial value after a loop in the parameter space, then the geometric gyrophase equals the solid angle spanned by the loop in the parameter space. This classical geometric gyrophase is compared with the geometric phase (the Berry phase) of the spin wave function of an electron placed in the same adiabatically changing magnetic field. Even though gyromotion is not the classical counterpart of the quantum spin, the similarities between the geometric phases of the two cases nevertheless reveal the similar geometric nature of the different physics laws governing these two physics phenomena.
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Sinitsyn, Nikolai
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Dark-field electron holography for the measurement of geometric phase.
Hÿtch, M J; Houdellier, F; Hüe, F; Snoeck, E
2011-07-01
The genesis, theoretical basis and practical application of the new electron holographic dark-field technique for mapping strain in nanostructures are presented. The development places geometric phase within a unified theoretical framework for phase measurements by electron holography. The total phase of the transmitted and diffracted beams is described as a sum of four contributions: crystalline, electrostatic, magnetic and geometric. Each contribution is outlined briefly and leads to the proposal to measure geometric phase by dark-field electron holography (DFEH). The experimental conditions, phase reconstruction and analysis are detailed for off-axis electron holography using examples from the field of semiconductors. A method for correcting for thickness variations will be proposed and demonstrated using the phase from the corresponding bright-field electron hologram. PMID:21864773
Spatially varying geometric phase in classically entangled vector beams of light
NASA Astrophysics Data System (ADS)
King-Smith, Andrew; Leary, Cody
We present theoretical results describing a spatially varying geometric (Pancharatnam) phase present in vector modes of light, in which the polarization and transverse spatial mode degrees of freedom exhibit classical entanglement. We propose an experimental setup capable of characterizing this effect, in which a vector mode propagates through a Mach-Zehnder interferometer with a birefringent phase retarder present in one arm. Since the polarization state of a classically entangled light beam exhibits spatial variation across the transverse mode profile, the phase retarder gives rise to a spatially varying geometric phase in the beam propagating through it. When recombined with the reference beam from the other interferometer arm, the presence of the geometric phase is exhibited in the resulting interference pattern. We acknowledge funding from the Research Corporation for Science Advancement by means of a Cottrell College Science Award.
Bruno, Patrick
2012-06-15
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined. PMID:23004240
Coherent cancellation of geometric phase for the OH molecule in external fields
NASA Astrophysics Data System (ADS)
Bhattacharya, M.; Marin, S.; Kleinert, M.
2014-05-01
The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.
On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems
NASA Astrophysics Data System (ADS)
Chen, Hsing-Ta; Reichman, David R.
2016-03-01
We perform extensive benchmark comparisons of surface hopping dynamics with numerically exact calculations for the spin-boson model over a wide range of energetic and coupling parameters as well as temperature. We find that deviations from golden-rule scaling in the Marcus regime are generally small and depend sensitively on the energetic bias between electronic states. Fewest switches surface hopping (FSSH) is found to be surprisingly accurate over a large swath of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic, at least for the case of an environment modeled with the commonly used Debye spectral density.
Two-phase fluid flow in geometric packing.
Paiva, Aureliano Sancho S; Oliveira, Rafael S; Andrade, Roberto F S
2015-12-13
We investigate how a plug of obstacles inside a two-dimensional channel affects the drainage of high viscous fluid (oil) when the channel is invaded by a less viscous fluid (water). The plug consists of an Apollonian packing with, at most, 17 circles of different sizes, which is intended to model an inhomogeneous porous region. The work aims to quantify the amount of retained oil in the region where the flow is influenced by the packing. The investigation, carried out with the help of the computational fluid dynamics package ANSYS-FLUENT, is based on the integration of the complete set of equations of motion. The study considers the effect of both the injection speed and the number and size of obstacles, which directly affects the porosity of the system. The results indicate a complex dependence in the fraction of retained oil on the velocity and geometric parameters. The regions where the oil remains trapped is very sensitive to the number of circles and their size, which influence in different ways the porosity of the system. Nevertheless, at low values of Reynolds and capillary numbers Re<4 and n(c)≃10(-5), the overall expected result that the volume fraction of oil retained decreases with increasing porosity is recovered. A direct relationship between the injection speed and the fraction of oil is also obtained. PMID:26527816
Geometric relativistic phase from Lorentz symmetry breaking effects in the cosmic string spacetime
NASA Astrophysics Data System (ADS)
Belich, H.; Bakke, K.
2016-04-01
In this paper, we have investigated the arising of geometric quantum phases in a relativistic quantum dynamics of a Dirac neutral particle from the spontaneous Lorentz symmetry violation effects in the cosmic string spacetime. We started by the Dirac equation in an effective metric, and we have observed a relativistic geometric phase which stems from the topology of the cosmic string spacetime and an intrinsic Lorentz symmetry breaking effects. It is shown that both Lorentz symmetry breaking effects and the topology of the defect yields a phase shift in the wave function of the nonrelativistic spin-1/2 particle.
Vibrational coherences in charge-transfer dyes: A non-adiabatic picture
NASA Astrophysics Data System (ADS)
Sissa, Cristina; Delchiaro, Francesca; Di Maiolo, Francesco; Terenziani, Francesca; Painelli, Anna
2014-10-01
Essential-state models efficiently describe linear and nonlinear spectral properties of different families of charge-transfer chromophores. Here, the essential-state machinery is applied to the calculation of the early-stage dynamics after ultrafast (coherent) excitation of polar and quadrupolar chromophores. The fully non-adiabatic treatment of coupled electronic and vibrational motion allows for a reliable description of the dynamics of these intriguing systems. In particular, the proposed approach is reliable even when the adiabatic and harmonic approximations do not apply, such as for quadrupolar dyes that show a multistable, broken-symmetry excited state. Our approach quite naturally leads to a clear picture for a dynamical Jahn-Teller effect in these systems. The recovery of symmetry due to dynamical effects is however disrupted in polar solvents where a static symmetry lowering is observed. More generally, thermal disorder in polar solvents is responsible for dephasing phenomena, damping the coherent oscillations with particularly important effects in the case of polar dyes.
Moving Difference (MDIFF) Non-adiabatic rapid sweep (NARS) EPR of copper(II)
Hyde, James S.; Bennett, Brian; Kittell, Aaron W.; Kowalski, Jason M.; Sidabras, Jason W.
2014-01-01
Non Adiabatic Rapid Sweep (NARS) EPR spectroscopy has been introduced for application to nitroxide-labeled biological samples (AW Kittell et al, (2011)). Displays are pure absorption, and are built up by acquiring data in spectral segments that are concatenated. In this paper we extend the method to frozen solutions of copper-imidazole, a square planar copper complex with four in-plane nitrogen ligands. Pure absorption spectra are created from concatenation of 170 5-gauss segments spanning 850 G at 1.9 GHz. These spectra, however, are not directly useful since nitrogen superhyperfine couplings are barely visible. Application of the moving difference (MDIFF) algorithm to the digitized NARS pure absorption spectrum is used to produce spectra that are analogous to the first harmonic EPR. The signal intensity is about 4 times higher than when using conventional 100 kHz field modulation, depending on line shape. MDIFF not only filters the spectrum, but also the noise, resulting in further improvement of the SNR for the same signal acquisition time. The MDIFF amplitude can be optimized retrospectively, different spectral regions can be examined at different amplitudes, and an amplitude can be used that is substantially greater than the upper limit of the field modulation amplitude of a conventional EPR spectrometer, which improves the signal-to-noise ratio of broad lines. PMID:24036469
Between ethylene and polyenes--the non-adiabatic dynamics of cis-dienes.
Kuhlman, Thomas S; Glover, William J; Mori, Toshifumi; Møller, Klaus B; Martínez, Todd J
2012-01-01
Using Ab Initio Multiple Spawning (AIMS) with a Multi-State Multi-Reference Perturbation theory (MS-MR-CASPT2) treatment of the electronic structure, we have simulated the non-adiabatic excited state dynamics of cyclopentadiene (CPD) and 1,2,3,4-tetramethyl-cyclopentadiene (Me4-CPD) following excitation to S1. It is observed that torsion around the carbon-carbon double bonds is essential in reaching a conical intersection seam connecting S1 and S0. We identify two timescales; the induction time from excitation to the onset of population transfer back to S0 (CPD: -25 fs, Me4-CPD: -71 fs) and the half-life of the subsequent population transfer (CPD: -28 fs, Me4-CPD: -48 fs). The longer timescales for Me4-CPD are a kinematic consequence of the inertia of the substituents impeding the essential out-of-plane motion that leads to the conical intersection seam. A bifurcation is observed on S1 leading to population transfer being attributable, in a 5 : 2 ratio for CPD and 7 : 2 ratio for Me4-CPD, to two closely related conical intersections. Calculated time-resolved photoelectron spectra are in excellent agreement with experimental spectra validating the simulation results. PMID:23230770
Non-Adiabatic, Multi-State Ring-Polymer Molecular Dynamics
NASA Astrophysics Data System (ADS)
Bell, Franziska; Menzeleev, Artur; Miller, Thomas, III
2014-03-01
Ring-polymer molecular dynamics (RPMD) has been shown to be a promising method for studying mechanisms and rates in large systems which require the inclusion of quantum effects, such as zero-point energies and tunneling. Examples involve electron and/or proton transfer reactions in enzymes and artificial catalysts. However, the traditional formulation of RPMD has several shortcomings: (i) it is restricted to migrations of only one distinguishable electron, (ii) it cannot describe photophysical processes, and (iii) it cannot be used in conjunction with potential energy surfaces obtained from electronic structure methods. Here I present a parameter-free extension of the RPMD method that addresses these issues and allows for the direct simulation of non-adiabatic processes involving many-electron wavefunctions without prior assumptions of the reaction mechanism. The new approach is demonstrated to provide a quantitative description of electron-transfer reaction rates and mechanisms throughout (i) the normal and inverted regimes and (ii) the weak- and strong-coupling regimes. I would like to thank the APS for financial support in form of a New Investigator Travel Award.
Vibrational coherences in charge-transfer dyes: A non-adiabatic picture
Sissa, Cristina; Delchiaro, Francesca; Di Maiolo, Francesco
2014-10-28
Essential-state models efficiently describe linear and nonlinear spectral properties of different families of charge-transfer chromophores. Here, the essential-state machinery is applied to the calculation of the early-stage dynamics after ultrafast (coherent) excitation of polar and quadrupolar chromophores. The fully non-adiabatic treatment of coupled electronic and vibrational motion allows for a reliable description of the dynamics of these intriguing systems. In particular, the proposed approach is reliable even when the adiabatic and harmonic approximations do not apply, such as for quadrupolar dyes that show a multistable, broken-symmetry excited state. Our approach quite naturally leads to a clear picture for a dynamical Jahn-Teller effect in these systems. The recovery of symmetry due to dynamical effects is however disrupted in polar solvents where a static symmetry lowering is observed. More generally, thermal disorder in polar solvents is responsible for dephasing phenomena, damping the coherent oscillations with particularly important effects in the case of polar dyes.
NASA Astrophysics Data System (ADS)
Heaps, Charles W.; Mazziotti, David A.
2016-08-01
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schrödinger equation with N Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from O ( N 2 ) to O ( N ) . By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing the nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems: the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations.
Suzuki-Trotter Formula for Real Time Dependent LDA II: Non-adiabatic MD
NASA Astrophysics Data System (ADS)
Miyamoto, Yoshiyuki; Sugino, Osamu
1998-03-01
In order to investigate ultrafast chemical reactions strongly coupled with electron dynamics, we must go beyond Born-Oppenheimer scheme. An ab-initio approach on this regime is quite challenging and applicable for many phenomena stimulated by electronic excitations. We have developed computational methods for a non-adiabatic molecular dynamics (MD) within the framework of the local density approximation (LDA) and pseudopotentials. The higher order Suziki-Trotter formula(M. Suzuki, J. Phys. Soc. Jpn. 61), L3015 (1992). for the time-evolution operator (e^fracihbarHΔ t) is found to be applicable even with use of separable non-local pseudopotentials(L. Kleinman, and D. M. Bylander, Phys. Rev. Lett. 48), 1425 (1982).. This formula enables us to perform numerically stable simulation for a long-time scale, during which orthonormality of wavefunctions is automatically conserved. At every time step, the Hellmann-Feynman force(J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C 12), 4409 (1979). on each atom is calculated to treat atomic motion within the classical Newton's equation. In this talk, a motion of an electronically excited K3 cluster is demonstrated as an example. During the simulation, sudden decrease of an expectation values of an excited electron is observed which can be attributed to non-radiative decay.
Geometric phase in entangled systems: A single-neutron interferometer experiment
Sponar, S.; Klepp, J.; Loidl, R.; Durstberger-Rennhofer, K.; Badurek, G.; Hasegawa, Y.; Filipp, S.; Bertlmann, R. A.; Rauch, H.
2010-04-15
The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [Phys. Rev. A 69, 032112 (2004)] and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2{radical}(2) and therefore always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like CHSH inequality, where S remains 2{radical}(2) for all settings of the geometric phase.
Minimal surfaces, incompressible flows and the geometric phase
NASA Astrophysics Data System (ADS)
Martinez, J. C.
1995-02-01
We show that the Berry phase may be associated with an incompressible flow issuing through a minimal surface. An example based on the linear Jahn-Teller effect is given and found to be related to a Clifford torus rather than the usual magnetic monopole in S 3.
Twisted geometries: A geometric parametrization of SU(2) phase space
Freidel, Laurent; Speziale, Simone
2010-10-15
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each face of its area, the two unit normals as seen from the two polyhedra sharing it, and an additional angle related to the extrinsic curvature. These quantities do not define a Regge geometry, since they include extrinsic data, but a looser notion of discrete geometry which is twisted in the sense that it is locally well-defined, but the local patches lack a consistent gluing among each other. We give the Poisson brackets among the new variables, and exhibit a symplectomorphism which maps them into the Poisson brackets of loop gravity. The new parametrization has the advantage of a simple description of the gauge-invariant reduced phase space, which is given by a product of phase spaces associated to edges and vertices, and it also provides an Abelianization of the SU(2) connection. The results are relevant for the construction of coherent states and, as a byproduct, contribute to clarify the connection between loop gravity and its subset corresponding to Regge geometries.
Geometric phase and gravitational precession of D-branes
NASA Astrophysics Data System (ADS)
Pedder, Chris; Sonner, Julian; Tong, David
2007-12-01
We study Berry’s phase in the D0-D4-brane system. When a D0-brane moves in the background of D4-branes, the first excited states undergo a holonomy described by a non-Abelian Berry connection. At weak coupling this is an SU(2) connection over R5, known as the Yang monopole. At strong coupling, the holonomy is recast as the classical gravitational precession of a spinning particle. The Berry connection is the spin connection of the near-horizon limit of the D4-branes, which is a continuous deformation of the Yang and anti-Yang monopole.
Geometric phases and quantum correlations dynamics in spin-boson model
Wu, Wei; Xu, Jing-Bo
2014-01-28
We explore the dynamics of spin-boson model for the Ohmic bath by employing the master equation approach and obtain an explicit expression of reduced density matrix. We also calculate the geometric phases of the spin-boson model by making use of the analytical results and discuss how the dissipative bosonic environment affects geometric phases. Furthermore, we investigate the dynamics of quantum discord and entanglement of two qubits each locally interacting with its own independent bosonic environments. It is found that the decay properties of quantum discord and entanglement are sensitive to the choice of initial state's parameter and coupling strength between system and bath.
An angular frequency dependence on the Aharonov–Casher geometric phase
Barboza, P.M.T.; Bakke, K.
2015-10-15
A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov–Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.
NASA Astrophysics Data System (ADS)
Acharya, Shree Ram; Baral, Nisha; Turkowski, Volodymyr; Rahman, Talat S.
2015-03-01
We apply Dynamical Mean-Field Theory (DMFT) to calculate the non-adiabatic (frequency-dependent) exchange-correlation kernel for the three-dimensional Hubbard model. We analyze the dependence of the kernel on the electron doping, local Coulomb repulsion and frequency by using three different impurity solvers: Hubbard-I, Iterative Perturbation Theory (IPT) and Continuous-Time Quantum Monte Carlo (CT-QMC). From the calculated data, we obtain approximate analytical expressions for the kernel. We apply the exact numerical and analytical kernels to study the non-equilibrium response of the system for applied ultrafast laser pulse. We demonstrate that the non-adiabaticity of the kernel plays an important role in the system response; in particular, leading to new excited-states involved in the system dynamics. Work supported in part by DOE Grant No. DOE-DE-FG02-07ER46354.
Demonstration of Geometric Landau-Zener Interferometry in a Superconducting Phase Qubit
NASA Astrophysics Data System (ADS)
Yu, Yang; Tan, Xinsheng; Zhang, Zhentao; Zhu, Shiliang; Zhang, Danwei; Han, Siyuan
2014-03-01
Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. Here we fill this gap by combining these two approaches in the study of the dynamics of a superconducting phase qubit. We propose and then experimentally demonstrate Landau-Zener interferometry based on pure geometric phases in this solid-state qubit. We observe the interference due to geometric phases accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is eliminated by a spin-echo pulse. Our numerical simulation results using measured energy relaxation and dephasing times agree well with the experimental results. The full controllability of the qubit population as a function of intrinsically fault-tolerant geometric phases provides a promising approach to fault-tolerant quantum computation. This work is partially supported by the SKPBR of China (2011CB922104, 2011CBA00200), NSFC (91021003, 11274156,11125417), PAPD, and the PCSIRT. Han is supported in part by NSF of United States (PHY-1314861).
Optimization of the Geometric Phase Sensitivity of an Array of Atom Ring Interferometers
NASA Astrophysics Data System (ADS)
Sandoval-Sanchez, Karina; Campo, Christian; Rivera, Tabitha; Toland, John
2015-05-01
Sagnac, and Aharonov-Bohm phase shifts are important geometric phase shifts in atom interferometry. These phase shifts characterize rotational and magnetic field interference effects respectively. Theoretical explorations have shown that a series of ring interferometers can be connected in series to increase the sensitivity of the overall device while keeping the maximum path separation less than the coherence length of the atoms. It has also been shown that the application of an area chirp to the rings will further enhance the sensitivity of the array of rings to geometric phase shifts. Area chirp refers to characterizing all of the rings in the array to a fixed percentage of a reference ring, this allows for the phase shifts in each ring to be characterized by one ring. The goal of this project is to determine a set of parameters namely kL, the product of the ring circumference and the wave number and γ, the chirp factor for the area chirp, that optimize the geometric phase sensitivity for an array of N rings. We model the transmission coefficient of a quantum matter wave through an area chirped array of interferometers as a function of phase, using transfer matrices to represent the transmission and reflection of individual rings in the array. Isolated transmission resonances represent the domain of interest, these are regions of high phase sensitivity. After optimizing a ring array without loss we apply velocity broadening to the input matter waves to investigate a more realistic output.
Dynamic and geometric phase accumulation by Gaussian-type modes in first-order optical systems.
Alieva, Tatiana; Bastiaans, Martin J
2008-08-01
Based on the ray transformation matrix formalism, we propose a simple method for the identification of the dynamic and geometric parts of the Gouy phase, acquired by an appropriate Gaussian-type beam while propagating through a first-order optical system. PMID:18670494
Geometric phase in cavity QED containing a nonlinear optical medium and a quantum well
NASA Astrophysics Data System (ADS)
Mohamed, A.-B. A.; Eleuch, H.
2015-11-01
The geometric phase (GP) in cavity QED filled with a nonlinear medium and containing a quantum well is analyzed. We observe collapses and revivals. The optical nonlinearity leads to high frequency oscillations of the GP. The GP is very sensitive not only to the dissipation rates but also to the amplitude of the laser pump.
Geometric phase of two-level atoms and thermal nature of de Sitter spacetime
NASA Astrophysics Data System (ADS)
Tian, Zehua; Jing, Jiliang
2013-04-01
In the framework of open quantum systems, we study the geometric phase acquired by freely falling and static two-level atoms interacting with quantized conformally coupled massless scalar fields in de Sitter-invariant vacuum. We find that, for the freely falling atom, the geometric phase gets a correction resulting from a thermal bath with the Gibbons-Hawking temperature, thus it clearly reveals the intrinsic thermal nature of de Sitter spacetime from a different physical context. For the static atom, there is a correction to the geometric phase coming from both the intrinsic thermal nature of de Sitter spacetime and the Unruh effect associated with the proper acceleration of the atom. Furthermore, in a gedanken experiment, we estimate the magnitude of the correction to the geometric phase as opposed to that in a flat spacetime. We find that the correction for the freely falling atom is too tiny to be measured, and that for the static atom achieves an observable magnitude only when the atom almost locates at the horizon.
Geometric phase of an atom inside an adiabatic radio-frequency potential
Zhang, P.; You, L.
2007-09-15
We investigate the geometric phase of an atom inside an adiabatic radio-frequency (rf) potential created from a static magnetic field (B field) and a time-dependent rf field. The spatial motion of the atomic center of mass is shown to give rise to a geometric phase, or Berry's phase, in the adiabatically evolving atomic hyperfine spin along the local B field. This phase is found to depend on both the static B field along the semiclassical trajectory of the atomic center of mass and an effective magnetic field consisting of the total B field, including the oscillating rf field. Specific calculations are provided for several recent atom interferometry experiments and proposals utilizing adiabatic rf potentials.
Fishman, Randy Scott; Haraldsen, Jason T
2011-01-01
While a magnetic phase may be both locally stable and globally unstable, global stability always implies local stability. The distinction between local and global stability is studied on a geometrically-frustrated triangular lattice antiferromagnet with easy axis, single-ion anisotropy D along the z axis. Whereas the critical value Dloc c for local stability may be discontinuous across a phase boundary, the critical value Dglo c Dloc c for global stability must be continuous. We demonstrate this behavior across the phase boundary between collinear 3 and 4 sublattice phases that are stable for large D.
Emergent excitation in the paramagnetic phase of geometrically frustrated GdMn2O5
NASA Astrophysics Data System (ADS)
Bukhari, Syed Hamad; Ahmad, Javed
2016-07-01
We have measured dielectric constant (ε) as well as magnetic susceptibility (χ) of GdMn2O5 in order to elucidate magnetoelectric phase transitions slightly above and below Néel temperature (TN). Our measurements clearly show that above TN there are short range magnetic correlations arising from geometrically frustrated Mn moments, which fluctuate with respect to field and frequency. These well-defined magnetoelectric phase transitions, together with other transitions below TN, have been observed and discussed in the light of the χ. Magnetoelectric phase diagram is drawn which corresponds well to polarization flip phenomenon as induced by 90° rotation of Gd moments in low temperature phase.
Fast non-Abelian geometric gates via transitionless quantum driving
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-01-01
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. PMID:26687580
Fast non-Abelian geometric gates via transitionless quantum driving
NASA Astrophysics Data System (ADS)
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-12-01
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
Fast non-Abelian geometric gates via transitionless quantum driving.
Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-01-01
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. PMID:26687580
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
NASA Astrophysics Data System (ADS)
Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo
2014-04-01
We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.
Geometric analysis of phase bunching in the central region of cyclotron
NASA Astrophysics Data System (ADS)
Miyawaki, Nobumasa; Fukuda, Mitsuhiro; Kurashima, Satoshi; Kashiwagi, Hirotsugu; Okumura, Susumu; Arakawa, Kazuo; Kamiya, Tomihiro
2013-07-01
An optimum condition for realizing phase bunching in the central region of a cyclotron was quantitatively clarified by a simplified geometric trajectory analysis of charged particles from the first to the second acceleration gap. The phase bunching performance was evaluated for a general case of a cyclotron. The phase difference of incident particles at the second acceleration gap depends on the combination of four parameters: the acceleration harmonic number h, the span angle θD of the dee electrode, the span angle θF from the first to the second acceleration gap, the ratio RV of the peak acceleration voltage between the cyclotron and ion source. Optimum values of θF for phase bunching were limited by the relationship between h and θD, which is 90°/h+θD/2≤θF≤180°/h+θD/2, and sin θF>0. The phase difference with respect to the reference particle at the second acceleration gap is minimized for voltage-ratios between two and four for an initial phase difference within 40 RF degrees. Although the slope of the first acceleration gap contributes to the RF phase at which the particles reach the second acceleration gap, phase bunching was not affected. An orbit simulation of the AVF cyclotron at the Japan Atomic Energy Agency verifies the evaluation based on geometric analysis.
NASA Astrophysics Data System (ADS)
Liu, Bao; Zhang, Feng-Yang; Song, Jie; Song, He-Shan
2015-06-01
We propose a direct measurement scheme to read out the geometric phase of a coupled double quantum dot system via a quantum point contact(QPC) device. An effective expression of the geometric phase has been derived, which relates the geometric phase of the double quantum dot qubit to the current through QPC device. All the parameters in our expression are measurable or tunable in experiment. Moreover, since the measurement process affects the state of the qubit slightly, the geometric phase can be protected. The feasibility of the scheme has been analyzed. Further, as an example, we simulate the geometrical phase of a qubit when the QPC device is replaced by a single electron transistor(SET).
NASA Astrophysics Data System (ADS)
Xue, Liyuan; Yu, Yanxia; Cai, Xiaoya; Pan, Hui; Wang, Zisheng
2016-01-01
We investigate time-dependent Pancharatnam phases and the relations between such geometric phases and quantum correlations, i.e., quantum discord and concurrence, of superconducting two-qubit coupling system in dissipative environment with the mixture effects of four different eigenstates of density matrix. We find that the time-dependent Pancharatnam phases not only keep the motion memory of such a two-qubit system, but also include the information of quantum correlations. We show that the sudden died and alive phenomena of quantum entanglement are intrinsic in the transition of Pancharatnam phase in the X-state and the complex oscillations of Pancharatnam phase in the Y-state. The faster the Pancharatnam phases change, the slower the quantum correlations decay. In particular, we find that a subspace of quantum entanglement can exist in the Y-state by choosing suitable coupling parameters between two-qubit system and its environment, or initial conditions.
NASA Astrophysics Data System (ADS)
Zhang, Kai; Nusran, N. M.; Slezak, B. R.; Gurudev Dutt, M. V.
2016-05-01
While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (∼10) operations. This occurs inspite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. We have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.
Krix, David; Nienhaus, Hermann
2014-08-21
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K{sub 2}O{sub 2} is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period.
NASA Astrophysics Data System (ADS)
Krix, David; Nienhaus, Hermann
2014-08-01
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K2O2 is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period.
Krix, David; Nienhaus, Hermann
2014-08-21
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K2O2 is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period. PMID:25149810
Cotton, Stephen J.; Miller, William H.
2013-12-21
A recently described symmetrical windowing methodology [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] for quasi-classical trajectory simulations is applied here to the Meyer-Miller [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] model for the electronic degrees of freedom in electronically non-adiabatic dynamics. Results generated using this classical approach are observed to be in very good agreement with accurate quantum mechanical results for a variety of test applications, including problems where coherence effects are significant such as the challenging asymmetric spin-boson system.
NASA Astrophysics Data System (ADS)
Mukherjee, Saikat; Adhikari, Satrajit
2014-08-01
We calculate the adiabatic potential energy surfaces (PESs) and the non-adiabatic coupling terms (NACTs) for the excited electronic states of K3 cluster by MRCI approach using MOLPRO. The NACTs are adapted with molecular symmetry to assign appropriate IREPs so that the elements of the Hamiltonian matrix are totally symmetric. We incorporate those NACTs into three-state adiabatic-to-diabatic transformation (ADT) equations to obtain ADT angles for constructing continuous, single-valued, smooth and symmetric diabatic Hamiltonian matrix, where its elements are fitted with analytic functions. Finally, we demonstrate that the dressed diabatic and adiabatic-via-dressed diabatic PECs show prominent topological effect over dressed adiabatic curves.
Orel, Ann E.; Miller, William H.
1980-11-01
A recently developed classical model for electronically nonadiabatic collision processes is applied to electronic-vibrational energy transfer in a collinear atom~diatom system, A + BC(v=1) + A*+ BC(v=0), which closely resembles Br-H{sub 2}. This classical model, which treats electronic as well as heavy particle (i.e., translation, rotation, and vibration) degrees of freedom by classical mechanics, is found to describe the resonance features in this process reasonably well. The usefulness of the approach is that it allows one to extend standard Monte Carlo classical trajectory methodology to include electronically non-adiabatic processes in a dynamically consistent way,
Quantum Entanglement and Geometric Phase of Two Moving Two-Level Atoms
NASA Astrophysics Data System (ADS)
Abdel-Khalek, S.
2015-09-01
An important kind of interaction between two moving two-level atoms and a field mode, where the coupling parameter is taken to be time-dependent, is presented in this paper. Nonlocal correlations between the atoms and the field have been investigated by means of concurrence and von Neumann entropy in terms of the involved parameters of the system. The results show that the atomic motion plays an essential role in the evolution of system dynamics, its nonlocal correlations and geometric phase. Moreover, an interesting correlation between the entanglement and the geometric phase during the evolution was observed. The presented system can be very useful for generating and maintaining high amount of entanglement by means of controlling the parameters of atomic motion.
Polarization conversion system with liquid-crystal geometric-phase-based cylindrical lens
NASA Astrophysics Data System (ADS)
Honma, Michinori; Nose, Toshiaki
2016-01-01
We demonstrate a polarization conversion system by utilizing the polarization-splitting function of a liquid-crystal (LC) geometric-phase-based cylindrical lens. The system was constructed by combining the LC lens with a partially rubbed cell. The operation principle includes the following two steps. (i) The incident light is first decomposed into right- and left-handed circularly polarized light (RCP and LCP, respectively) as an attribute of geometric-phase-based optical elements. (ii) Then, only the RCP light is transformed into LCP light by passing it through the partially rubbed cell; as a result, the incident unpolarized light is converted into LCP light. We experimentally reveal the feasibility of the system by evaluating the effects, on the polarization conversion capability, of the diffraction efficiency, focal length, and partially rubbed cell’s retardation. The polarization conversion efficiency was obtained to be 65% on average for 400-700 nm and a maximum of 79% at 610 nm.
NASA Astrophysics Data System (ADS)
Akopyan, M. E.; Baturo, V. V.; Lukashov, S. S.; Poretsky, S. A.; Pravilov, A. M.
2012-06-01
The stepwise two-step two-color and three-step three-color laser excitation schemes are used for selective population of rovibronic levels of the first-tier ion-pair E0_g^ + and D0_u^ + states of molecular iodine and studies of non-adiabatic transitions to the D and E states induced by collisions with M = I2(X) and H2O. Collection and analysis of the luminescence after excitation of the vE = 8, 13 and vD = 13, 18 vibronic levels of the E and D states in the pure iodine vapor and the gas-phase mixtures with H2O provide rate constants for the non-adiabatic transitions to the D and E state induced by collisions with these molecules. Vibrational distributions for the I2(E,v_E {longleftrArr} limits^M D,v_D ) collision-induced non-adiabatic transitions (CINATs) are obtained. Rather strong λ _{lum}^{max } ≈ 3400 Å luminescence band is observed in the I2 + H2O mixtures, whereas its intensity is ˜100 times less in pure iodine vapor. Radiative lifetimes and quenching rate constants of the I2(E,vE = 8, 13 and D,vD = 13, 18) vibronic state are also determined. Rate constants of the I2(E,v_E stackrel {I_2 (X)} { to 30pt {rArrfill}} D,v_D ), vE = 8-54, CINATs are measured again and compared with those obtained earlier. New data confirm resonance characters of the CINATs found in our laboratory about 10 years ago. Possible reasons of differences between rate constant values obtained in this and earlier works are discussed. It is shown, in particular, that differences in rate constants of non-resonant CINATs are due to admixture of water vapor in iodine.
Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases
NASA Astrophysics Data System (ADS)
Ota, Yukihiro; Goto, Yoshito; Kondo, Yasushi; Nakahara, Mikio
2009-11-01
A proposal for applying nonadiabatic geometric phases to quantum computing, called double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A 67, 022319 (2003)], is demonstrated in a liquid-state nuclear magnetic-resonance quantum computer. Using a spin-echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision nuclear magnetic-resonance system for chemical analysis. We show that a dynamical phase is successfully eliminated and a one-qubit quantum gate is realized although the gate fidelity is not high.
A non-adiabatic dynamics study of octatetraene: the radiationless conversion from S2 to S1.
Qu, Zexing; Liu, Chungen
2013-12-28
Simulation of the excited state dynamics of all-trans-1,3,5,7-octatetraene has been performed to investigate the ultrafast radiationless S2 → S1 internal conversion process. Multireference configuration interaction with single excitation method has been employed to optimize the equilibrium structure of the excited states, as well as the S2/S1 conical intersection, and to investigate the non-adiabatic molecular dynamics of the S2/S1 state transition. At the conical intersection, the molecule is found to be distorted from the original planar trans structure to a nearly perpendicular conformation around C3-C4 bond, with the torsion angle being about 107°. Such structural change can result in mutual approaching of states S2 and S1 in energy, and drastically increase the nonadiabatic coupling between the two states by destroying the inter-state symmetry prohibition in the electronic wavefunctions. Surface-hopping molecular dynamics simulations are performed to describe the non-adiabatic process. Upon the Franck-Condon excitation to the S2 state, the molecule quickly twists its C3-C4 bond and approaches the conical intersection region, where it can undergo efficient internal conversion to S1. The decay time constant (τ) of S2 state is estimated to be around 251 fs by fitting the occupation number of average fraction of trajectories using an exponential damping function. This value is reasonably consistent with previous experimental measurements of around 300-400 fs. PMID:24387367
NASA Astrophysics Data System (ADS)
Pedrosa, Inácio A.; Melo, Jilvan L.; Salatiel, Sadoque
2014-11-01
We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system's quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry's phase.
Multi-target-qubit unconventional geometric phase gate in a multi-cavity system
NASA Astrophysics Data System (ADS)
Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping
2016-02-01
Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits.
Multi-target-qubit unconventional geometric phase gate in a multi-cavity system.
Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping
2016-01-01
Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits. PMID:26898176
NASA Astrophysics Data System (ADS)
Dai, Xianglu; Xie, Huimin; Wang, Qinghua
2014-06-01
The geometric phase analysis (GPA), an important image-based deformation measurement method, has been used at both micro- and nano-scale. However, when a deformed image has apparent distortion, non-ignorable error in the obtained deformation field could occur by using this method. In this paper, the geometric phase analysis based on the windowed Fourier transform (WFT) is proposed to solve the above-mentioned issue, defined as the WFT-GPA method. In WFT-GPA, instead of the Fourier transform (FT), the WFT is utilized to extract the phase field block by block, and therefore more accurate local phase information can be acquired. The simulation tests, which include detailed discussion of influence factors for measurement accuracy such as window size and image noise, are conducted with digital deformed grids. The results verify that the WFT-GPA method not only keeps all advantages of traditional GPA method, but also owns a better accuracy for deformation measurement. Finally, the WFT-GPA method is applied to measure the machining distortion incurred in soft ultraviolet nanoimprint lithography (UV-NIL) process. The successful measurement shows the feasibility of this method and offers a full-field way for characterizing the replication quality of UV-NIL process.
Multi-target-qubit unconventional geometric phase gate in a multi-cavity system
Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping
2016-01-01
Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits. PMID:26898176
Kittell, Aaron W.; Camenisch, Theodore G.; Ratke, Joseph J.; Sidabras, Jason W.; Hyde, James S.
2011-01-01
A continuous wave (CW) electron paramagnetic resonance (EPR) spectrum is typically displayed as the first harmonic response to the application of 100 kHz magnetic field modulation, which is used to enhance sensitivity by reducing the level of 1/f noise. However, magnetic field modulation of any amplitude causes spectral broadening and sacrifices EPR spectral intensity by at least a factor of two. In the work presented here, a CW rapid-scan spectroscopic technique that avoids these compromises and also provides a means of avoiding 1/f noise is developed. This technique, termed non-adiabatic rapid sweep (NARS) EPR, consists of repetitively sweeping the polarizing magnetic field in a linear manner over a spectral fragment with a small coil at a repetition rate that is sufficiently high that receiver noise, microwave phase noise, and environmental microphonics, each of which has 1/f characteristics, are overcome. Nevertheless, the rate of sweep is sufficiently slow that adiabatic responses are avoided and the spin system is always close to thermal equilibrium. The repetitively acquired spectra from the spectral fragment are averaged. Under these conditions, undistorted pure absorption spectra are obtained without broadening or loss of signal intensity. A digital filter such as a moving average is applied to remove high frequency noise, which is approximately equivalent in bandwidth to use of an integrating time constant in conventional field modulation with lock-in detection. Nitroxide spectra at L- and X-band are presented. PMID:21741868
Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Shi, Qian-Qian; Wang, Hong-Lei; Li, Sheng-Hao; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang
2016-06-01
Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.
Analytical calculation of spectral phase of grism pairs by the geometrical ray tracing method
NASA Astrophysics Data System (ADS)
Rahimi, L.; Askari, A. A.; Saghafifar, H.
2016-07-01
The most optimum operation of a grism pair is practically approachable when an analytical expression of its spectral phase is in hand. In this paper, we have employed the accurate geometrical ray tracing method to calculate the analytical phase shift of a grism pair, at transmission and reflection configurations. As shown by the results, for a great variety of complicated configurations, the spectral phase of a grism pair is in the same form of that of a prism pair. The only exception is when the light enters into and exits from different facets of a reflection grism. The analytical result has been used to calculate the second-order dispersions of several examples of grism pairs in various possible configurations. All results are in complete agreement with those from ray tracing method. The result of this work can be very helpful in the optimal design and application of grism pairs at various configurations.
Reimers, Jeffrey R; McKemmish, Laura K; McKenzie, Ross H; Hush, Noel S
2015-10-14
Using a simple model Hamiltonian, the three correction terms for Born-Oppenheimer (BO) breakdown, the adiabatic diagonal correction (DC), the first-derivative momentum non-adiabatic correction (FD), and the second-derivative kinetic-energy non-adiabatic correction (SD), are shown to all contribute to thermodynamic and spectroscopic properties as well as to thermal non-diabatic chemical reaction rates. While DC often accounts for >80% of thermodynamic and spectroscopic property changes, the commonly used practice of including only the FD correction in kinetics calculations is rarely found to be adequate. For electron-transfer reactions not in the inverted region, the common physical picture that diabatic processes occur because of surface hopping at the transition state is proven inadequate as the DC acts first to block access, increasing the transition state energy by (ℏω)(2)λ/16J(2) (where λ is the reorganization energy, J the electronic coupling and ω the vibration frequency). However, the rate constant in the weakly-coupled Golden-Rule limit is identified as being only inversely proportional to this change rather than exponentially damped, owing to the effects of tunneling and surface hopping. Such weakly-coupled long-range electron-transfer processes should therefore not be described as "non-adiabatic" processes as they are easily described by Born-Huang ground-state adiabatic surfaces made by adding the DC to the BO surfaces; instead, they should be called just "non-Born-Oppenheimer" processes. The model system studied consists of two diabatic harmonic potential-energy surfaces coupled linearly through a single vibration, the "two-site Holstein model". Analytical expressions are derived for the BO breakdown terms, and the model is solved over a large parameter space focusing on both the lowest-energy spectroscopic transitions and the quantum dynamics of coherent-state wavepackets. BO breakdown is investigated pertinent to: ammonia inversion, aromaticity
Geometric phase for a neutral particle in the presence of a topological defect
NASA Astrophysics Data System (ADS)
Bakke, K.; Nascimento, J. R.; Furtado, C.
2008-09-01
In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.
A geometric entropy detecting the Erdös-Rényi phase transition
NASA Astrophysics Data System (ADS)
Franzosi, Roberto; Felice, Domenico; Mancini, Stefano; Pettini, Marco
2015-07-01
We propose a method to associate a differentiable Riemannian manifold to a generic many-degrees-of-freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical statistical mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the “giant component” according to the Erdös-Rényi theorem.
Geometric phase low-coherence interference microscopy at high numerical apertures
NASA Astrophysics Data System (ADS)
Roy, Maitreyee; Svahn, Peter; Sheppard, Colin J. R.
2001-09-01
A low-coherence Linnik interference microscope using high numerical aperture optics has been constructed. The system uses a tungsten halogen lamp and a Koehler illumination, with separate control over field and aperture stops, so that experiments can be conducted with a range of different geometric phase which is achieved by using a polarizing beam splitter, a quarter wave plate and a rotating polarizer. Image information is extracted from the visibility of the fringes, and the position of the visibility peak along the scanning axis, yielding the height of the test surface at the corresponding points.
Generation of equal-intensity coherent optical beams by binary geometrical phase on metasurface
NASA Astrophysics Data System (ADS)
Wang, Zheng-Han; Jiang, Shang-Chi; Xiong, Xiang; Peng, Ru-Wen; Wang, Mu
2016-06-01
We report here the design and realization of a broadband, equal-intensity optical beam splitter with a dispersion-free binary geometric phase on a metasurface with unit cell consisting of two mirror-symmetric elements. We demonstrate experimentally that two identical beams can be efficiently generated with incidence of any polarization. The efficiency of the device reaches 80% at 1120 nm and keeps larger than 70% in the range of 1000-1400 nm. We suggest that this approach for generating identical, coherent beams have wide applications in diffraction optics and in entangled photon light source for quantum communication.
Phase Diagram of a Geometrically-Frustrated Triangular-Lattice Antiferromagnet in a Magnetic Field
Fishman, Randy Scott
2011-01-01
The magnetic phase diagram of a geometrically-frustrated triangular-lattice antiferromagnet is evaluated as a function of external magnetic field and anisotropy using a trial spin state built from harmonics of a fundamental ordering wavevector. A non-collinear incommensurate state, observed to be chiral and ferroelectric in CuFeO2, is sandwiched between a collinear state with 4 sublattices (SLs) and a 5-SL state. Chiral and non-collinear 5-SL states are predicted to appear at fields above and below the collinear 5-SL states.
Non-adiabatic and adiabatic transitions at level crossing with decay: two- and three-level systems
NASA Astrophysics Data System (ADS)
Kenmoe, M. B.; Mkam Tchouobiap, S. E.; Kenfack Sadem, C.; Tchapda, A. B.; Fai, L. C.
2015-03-01
We investigate the Landau-Zener (LZ) like dynamics of decaying two- and three-level systems with decay rates {{Γ }1} and {{Γ }2} for levels with minimum and maximum spin projection. Non-adiabatic and adiabatic transition probabilities are calculated from diabatic and adiabatic bases for two- and three-level systems. We extend the familiar two-level model of atoms with decay from the excited state out of the system into the hierarchy of three-level models which can be solved analytically or computationally in a non-perturbative manner. Exact analytical solutions are obtained within the framework of an extended form of the proposed procedure which enables to take into account all possible initial moments rather than large negative time {{t}0}=-∞ as in standard LZ problems. We elucidate the applications of our results from a unified theoretical basis that numerically analyzes the dynamics of a system as probed by experiments.
Miller, William H. Cotton, Stephen J.
2015-04-07
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employed in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time.
Taioli, Simone; Garberoglio, Giovanni; Simonucci, Stefano; Beccara, Silvio a; Aversa, Lucrezia; Nardi, Marco; Verucchi, Roberto; Iannotta, Salvatore; Dapor, Maurizio; and others
2013-01-28
In this work, we investigate the processes leading to the room-temperature growth of silicon carbide thin films by supersonic molecular beam epitaxy technique. We present experimental data showing that the collision of fullerene on a silicon surface induces strong chemical-physical perturbations and, for sufficient velocity, disruption of molecular bonds, and cage breaking with formation of nanostructures with different stoichiometric character. We show that in these out-of-equilibrium conditions, it is necessary to go beyond the standard implementations of density functional theory, as ab initio methods based on the Born-Oppenheimer approximation fail to capture the excited-state dynamics. In particular, we analyse the Si-C{sub 60} collision within the non-adiabatic nuclear dynamics framework, where stochastic hops occur between adiabatic surfaces calculated with time-dependent density functional theory. This theoretical description of the C{sub 60} impact on the Si surface is in good agreement with our experimental findings.
Miller, William H.; Orel, Ann E.
1980-11-01
A classical interpretation of the Dirac-Van Vleck spin version of valence bond theory is used to obtain a classical model for electronic degrees of freedom within the valence bond framework. The approach is illustrated by deriving the explicit forms of the classical Hamiltonians, involving electronic and heavy particle degrees of freedom, for the H-H{sub 2}, F-H{sub 2} , and O-H{sub 2} systems. It is also shown how the initial conditions for both electronic and heavy particle degrees of freedom are chosen to carry out a classical trajectory simulation of collision processes. The attractive feature of this model is that it is as eaaily applicable to electronically non-adiabatic processes as it is to adiabatic ones.
Piezoelectric control of the mobility of a domain wall driven by adiabatic and non-adiabatic torques
NASA Astrophysics Data System (ADS)
de Ranieri, E.; Roy, P. E.; Fang, D.; Vehsthedt, E. K.; Irvine, A. C.; Heiss, D.; Casiraghi, A.; Campion, R. P.; Gallagher, B. L.; Jungwirth, T.; Wunderlich, J.
2013-09-01
The rich internal degrees of freedom of magnetic domain walls make them an attractive complement to electron charge for exploring new concepts of storage, transport and processing of information. Here we use the tunable internal structure of a domain wall in a perpendicularly magnetized GaMnAsP/GaAs ferromagnetic semiconductor and demonstrate devices in which piezoelectrically controlled magnetic anisotropy yields up to 500% mobility variations for an electrical-current-driven domain wall. We observe current-induced domain wall motion over a wide range of current-pulse amplitudes and report a direct observation and the piezoelectric control of the Walker breakdown separating two regimes with different mobilities. Our work demonstrates that in spin-orbit-coupled ferromagnets with weak extrinsic domain wall pinning, the piezoelectric control allows one to experimentally assess the upper and lower boundaries of the characteristic ratio of adiabatic and non-adiabatic spin-transfer torques in the current-driven domain wall motion.
NASA Astrophysics Data System (ADS)
Tiwari, Vivek
2015-05-01
Understanding the fundamental physics of light-harvesting in both, natural and artificial systems is key for the development of efficient light-harvesting technologies. My thesis addresses the following topics, i.) the mechanism underlying the remarkably efficient electronic energy transfer in natural light harvesting antennas, ii.) a femtosecond time-resolved photonumeric technique to quantitatively characterize transient chemical species. This talk will concentrate on the first project, while briefly touching the key ideas of the second project. Light harvesting antennas use a set of closely spaced pigment molecules held in a controlled relative geometry by a protein. It is shown that in certain antenna proteins the excited state electronic energy gaps between the pigments are resonant with a quantum of pigment vibrational energy. With such a vibrational-electronic resonance, anti-correlated motions between the pigments lead to a strong coupling between the electronic and nuclear motions, that is, breakdown of the Born-Oppenheimer approximation, over a wide range of pigment vibrational motions. It is shown that the 2D spectroscopic signatures of the resulting unavoidable nested non-adiabatic energy funnel on the excited states of photosynthetic antennas are consistent with all the reported 2D signatures of long-lived coherent oscillations, including the ones that are not explained by prior models of excited state electronic energy transfer. Extensions that account for both resonant and near-resonant pigment vibrations suggest that photosynthetic energy transfer presents a novel design in which electronic energy transfer proceeds non-adiabatically through clusters of vibrations with frequencies distributed around electronic energy gaps. I will also briefly talk about our experiments demonstrating quantitative time-resolved measurement of absolute number of excited state molecules. Based on these measurements, an all-optical technique that simultaneously determines
Phase transition of charged Black Holes in Brans-Dicke theory through geometrical thermodynamics
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Panahiyan, S.; Panah, B. Eslam; Armanfard, Z.
2016-07-01
In this paper, we take into account black hole solutions of Brans-Dicke-Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and compare its results with those, calculated in the canonical ensemble through heat capacity. We show that these black holes enjoy second order phase transitions. We also show that there is a lower bound for the horizon radius of physical charged black holes in Brans-Dicke theory, which originates from restrictions of positivity of temperature. In addition, we find that employing a specific thermodynamical metric in the context of geometrical thermodynamics yields divergencies for the thermodynamical Ricci scalar in places of the phase transitions. It will be pointed out that due to the characteristic behavior of the thermodynamical Ricci scalar around its divergence points, one is able to distinguish the physical limitation point from the phase transitions. In addition, the free energy of these black holes will be obtained and its behavior will be investigated. It will be shown that the behavior of the free energy in the place where the heat capacity diverges demonstrates second order phase transition characteristics.
Trugenberger, Carlo A
2015-12-01
Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension d(H)=4. The model has a geometric quantum phase transition with disorder parameter (d(H)-d(s)), where d(s) is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions. PMID:26764755
Group theoretical Laws and Geometrical Phase for Paraxial Self-focusing and Solitons
NASA Astrophysics Data System (ADS)
Dantu, Subbarao; Uma, R.
1998-11-01
Group theoretical laws are formulated for the dynamics of paraxial self-focusing and soliton dynamics. The close similarity in the dynamical formulation of the theory of paraxial self-focusing of cylindrical laser beams of circular as well as elliptical cross-sections and paraxial solitons is exploited to state the group theoretical laws for the dynamics which in their limited form are known as ABCD laws in optics using our recent formulation of one of these phenomena^1. The dynamics of the laser beam is in terms of its evolution in the direction propagation while the soliton dynamics is along the actual time axis. (Conceiving soliton dynamics similar to a planar beam in the x-t plane, it can be analyzed using the paraxial approximation.) The group governing the dynamics is shown to be the Lorentz group, which gets reduced to the rotation group in the absorption-less case. Geometrical phase is evaluated for all these beams and solitons using our recent formulation of the geometric phase in projective space^2. 1. D. Subbarao, R. Uma and H. Singh, Phys. Plasmas, 5, Aug. (1998). 2. D.Subbarao Opt. Lett. 20, 2162 (1995) The authors acknowledge the financial support of CSIR(India) under the project 03(0815)/97/EMR-II for this work.
Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism
NASA Astrophysics Data System (ADS)
Trugenberger, Carlo A.
2015-12-01
Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.
Application of geometric phase to wavefront sensing for astronomical adaptive optics
NASA Astrophysics Data System (ADS)
Bloemhof, E. E.
2014-02-01
Modern adaptive optics systems give high performance, both in terms of Strehl ratio (degree of correction) and corrected field of view. Arguably the most important subsystem is the wavefront sensor, which measures the deviation from flatness of the incident wavefront that has been perturbed by the turbulent atmosphere, and commands an actuated mirror to compensate. An aspect of the wavefront sensor essential to achieving high sensitivity is that it perform over a broad spectral bandwidth; operation without correction for guide star color is also desirable. With this in mind, wavefront sensors are considered that make use of the geometric (or topological) phase, which has the property that the value of the phase is independent of wavelength. Conceptual system designs and advantages are discussed.
Geometrical aspects of the frustration in the cubic phases of lyotropic liquid crystals.
Anderson, D M; Gruner, S M; Leibler, S
1988-01-01
Bicontinuous cubic phases, composed of bilayers arranged in the geometries of periodic minimal surfaces, are found in a variety of different lipid/water systems. It has been suggested recently that these cubic structures arrive as the result of competition between two free-energy terms: the curvature energy of each monolayer and the stretching energy of the lipid chains. This scenario, closely analogous to the one that explains the origin of the hexagonal phases, is investigated here by means of simple geometrical calculations. It is first assumed that the lipid bilayer is of constant thickness and the distribution of the (local) mean curvature of the phospholipid-water interfaces is calculated. Then, assuming the mean curvature of these interfaces is constant, the distribution of the bilayer's thickness is calculated. Both calculations quantify the fact that the two energy terms are frustrated and cannot be satisfied simultaneously. However, the amount of the frustration can be smaller for the cubic phase than for the lamellar and hexagonal structures. Therefore, this phase can appear in the phase diagram between the other two, as observed in many recent experiments. PMID:3399497
Viennot, David
2010-10-15
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-Abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We apply this formalism to describe the non-Abelian geometric phase (when the geometric phase generator does not commute with the dynamical phase generator). We find then an assumption to obtain a new kind of separation between the dynamical and the geometric phases. We also apply this formalism to the gauge theory of gravity in the presence of a Dirac spinor field in order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.
Non-radial, non-adiabatic solar-like oscillations in RGB and HB stars
NASA Astrophysics Data System (ADS)
Grosjean, M.; Dupret, M. A.; Belkacem, K.; Montalbán, J.; Noels, A.; Samadi, R.
2013-03-01
CoRoT and Kepler observations of red giants reveal rich spectra of non-radial solar-like oscillations allowing to probe their internal structure. We compare the theoretical spectrum of two red giants in the same region of the HR diagram but in different evolutionary phases. We present here our first results on the inertia, lifetimes and amplitudes of the oscillations and discuss the differences between the two stars.
NASA Astrophysics Data System (ADS)
Wójcik, P.; Zegrodnik, M.; Rzeszotarski, B.; Adamowski, J.
2016-09-01
The tunneling conductance through the half-metal/conical magnet/superconductor (HM/CM/SC) junctions is investigated with the use of the Bogoliubov-de Gennes equations in the framework of Blonder-Tinkham-Klapwijk formalism. Due to the spin band separation in the HM, the conductance in the subgap region is mainly determined by the anomalous Andreev reflection, the probability of which strongly depends on the spin transmission in the CM layer. We show that the spins of electrons injected from the HM can be transmitted through the CM to the SC either adiabatically or non-adiabatically depending on the period of the spatial modulation of the exchange field. We find that the conductance in the subgap region oscillates as a function of the CM layer thickness wherein the oscillations transform from the irregular pattern in the non-adiabatic regime to the regular one in the adiabatic regime. For both adiabatic and non-adiabatic transport regimes the conductance is studied over a broad range of parameters determining the spiral magnetization in the CM. We find that in the non-adiabatic regime, the decrease of the exchange field amplitude in the CM leads to the emergence of the conductance peak for the particular CM thickness in agreement with recent experiments.
Phase-space-region operators and the Wigner function: Geometric constructions and tomography
NASA Astrophysics Data System (ADS)
Ellinas, Demosthenes; Bracken, Anthony J.
2008-11-01
Quasiprobability measures on a canonical phase space give rise through the action of Weyl’s quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations.
Geometric phase of a spin-1 2 particle coupled to a quantum vector operator
NASA Astrophysics Data System (ADS)
Aguilar, Pedro; Chryssomalakos, Chryssomalis; Guzmán, Edgar
2016-05-01
We calculate Berry’s phase when the driving field, to which a spin-1 2 is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in general, components, e.g. the angular momentum of another particle, or another spin. The geometric phase of the entire system, spin plus “quantum driving field”, is first computed, and is then subdivided into the two subsystems, using the Schmidt decomposition of the total wave function — the resulting expression shows a marked, purely quantum effect, involving the commutator of the field components. We also compute the corresponding mean “classical” phase, involving a precessing magnetic field in the presence of noise, up to terms quadratic in the noise amplitude — the results are shown to be in excellent agreement with numerical simulations in the literature. Subtleties in the relation between the quantum and classical case are pointed out, while three concrete examples illustrate the scope and internal consistency of our treatment.
Kaestner, Bernd; Kashcheyevs, Vyacheslavs
2015-10-01
Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property--the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of [Formula: see text] as function of control parameters, where [Formula: see text] is the electron charge and f is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These devices allow modulation of charge exchange rates between the dot and the leads over many orders of magnitude and enable trapping of a precise number of electrons far away from equilibrium with the leads. The corresponding non-adiabatic pumping protocols focus on understanding of separate parts of the pumping cycle associated with charge loading, capture and release. In this report we review realizations, models and metrology applications of quantized charge pumps based on tunable-barrier quantum dots. PMID:26394066
De Ranieri, E; Roy, P E; Fang, D; Vehsthedt, E K; Irvine, A C; Heiss, D; Casiraghi, A; Campion, R P; Gallagher, B L; Jungwirth, T; Wunderlich, J
2013-09-01
The rich internal degrees of freedom of magnetic domain walls make them an attractive complement to electron charge for exploring new concepts of storage, transport and processing of information. Here we use the tunable internal structure of a domain wall in a perpendicularly magnetized GaMnAsP/GaAs ferromagnetic semiconductor and demonstrate devices in which piezoelectrically controlled magnetic anisotropy yields up to 500% mobility variations for an electrical-current-driven domain wall. We observe current-induced domain wall motion over a wide range of current-pulse amplitudes and report a direct observation and the piezoelectric control of the Walker breakdown separating two regimes with different mobilities. Our work demonstrates that in spin-orbit-coupled ferromagnets with weak extrinsic domain wall pinning, the piezoelectric control allows one to experimentally assess the upper and lower boundaries of the characteristic ratio of adiabatic and non-adiabatic spin-transfer torques in the current-driven domain wall motion. PMID:23749266
NASA Astrophysics Data System (ADS)
Kaestner, Bernd; Kashcheyevs, Vyacheslavs
2015-10-01
Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property—the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of {{q}\\text{e}} f as function of control parameters, where {{q}\\text{e}} is the electron charge and f is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These devices allow modulation of charge exchange rates between the dot and the leads over many orders of magnitude and enable trapping of a precise number of electrons far away from equilibrium with the leads. The corresponding non-adiabatic pumping protocols focus on understanding of separate parts of the pumping cycle associated with charge loading, capture and release. In this report we review realizations, models and metrology applications of quantized charge pumps based on tunable-barrier quantum dots.
Geometrical phase and inertial regime of the magnetization: Hannay angle and magnetic monopole
NASA Astrophysics Data System (ADS)
Wegrowe, J.-E.; Olive, E.
2015-09-01
It is well known that the Landau-Lifshitz-Gilbert (LLG) equation for a macroscopic magnetic moment find its limit of validity at very short time scales or equivalently at very high frequencies. The reason for this limit of validity is well understood in terms of separation of the characteristic times between slow (the magnetization) and fast (the environment) degrees of freedom, as pointed-out in the stochastic derivation of the LLG equation first proposed by W. F. Brown in 1963. Indeed, the ferromagnetic moment is a slow collective variable, but fast degrees of freedom are also playing a role in the dynamics, and especially the variation of the angular momentum responsible for inertia. In the last couple of years, the generalization of the LLG equation with inertia (ILLG) has been derived by different means (see list of references). The signature of the inertial regime of the magnetization is the nutation that can be measured by resonance experiments (but it has not been observed up to know). We developed an approach in terms of geometrical phase (defining the corresponding Hannay angle, which is the classical analog to the quantum Berry phase: see references), that has recently been used with success to analogous problems. We calculated the Hannay angle for the precession of the magnetization in the case of the inertial effect, and the corresponding magnetic monopole. This analysis allows the slow vs. fast variable expansion to be calculated in the specific case of pure precession.
Kubař, Tomáš; Elstner, Marcus
2013-04-28
In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed. PMID:23493847
Complex defect in pyrite and its structure model derived from geometric phase analysis.
Németh, Péter; Dódony, István; Pósfai, Mihály; Buseck, Peter R
2013-10-01
New methods for defect analysis can lead to improved interpretation of experimental data and thus better understanding of material properties. Although transmission electronmicroscopy (TEM) has been used to study defects for many decades, interpretive ambiguities can arise for cases that seem simple or even trivial.Using geometric phase analysis (GPA), an image processing procedure, we show that an apparent simple line defect in pyrite has an entirely different character. It appears to be a b = ½[100] edge dislocation as viewed in a [001] high-resolution TEM (HRTEM) image, but the measured u(x) and u(y) displacements are asymmetric, which is inconsistent with a simple line dislocation. Instead, the defect is best understood as a terminating {101} marcasite slab in pyrite. The simulated HRTEM image based on this model reproduces the defect contrast and illustrates the power of GPA analysis for (1) avoiding potential pitfalls of misinterpreting apparently simple defects in HRTEM images, (2) detecting differences in elastic properties at the atomic scale, and (3) providing data for the positions of atom columns, thereby facilitating the construction of structure models for complex defects. PMID:23773546
Molecular level crossing and the geometric phase effect from the optical Hanle perspective
NASA Astrophysics Data System (ADS)
Glenn, R.; Dantus, M.
2016-04-01
Level-crossing spectroscopy involves lifting the degeneracy of an excited state and using the interference of two nearly degenerate levels to measure the excited-state lifetime. Here we use the idea of interference between different pathways to study the momentum-dependent wave-packet lifetime due an excited-state level crossing (conical intersection) in a molecule. Changes in population from the wave-packet propagation are reflected in the detected fluorescence. We use a chirped pulse to control the wave-packet momentum. Increasing the chirp rate increases the transition to the lower state through the conical intersection. It also increases the interference of different pathways in the upper electronic state due to the geometric phase acquired. Therefore, increasing the chirp rate decreases the population of the upper electronic state and its fluorescence yield. This suggests that there is a finite momentum-dependent lifetime of the wave packet through the level crossing as a function of chirp. We dub this lifetime the wave-packet-momentum lifetime.
Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap
Berrada, K.; Ooi, C. H. Raymond; Abdel-Khalek, S.
2015-03-28
Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and anti-Stokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times. This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.
Sanz-Sanz, Cristina; Aguado, Alfredo; Roncero, Octavio; Naumkin, Fedor
2015-12-21
Analytical derivatives and non-adiabatic coupling matrix elements are derived for Hn (+) systems (n = 3-5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H3 (+)) or triatomics-in-molecules (for H4 (+) and H5 (+)) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate H2(v(')=0,j(')=0)+H2 (+)(v,j=0) collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H2 (+) are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H2 (+) reactant and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, is discussed in terms of the long range behaviour of the interaction potential which is properly described within the triatomics-in-molecules formalism. PMID:26696058
Sanz-Sanz, Cristina; Aguado, Alfredo; Roncero, Octavio; Naumkin, Fedor
2016-01-01
Analytical derivatives and non-adiabatic coupling matrix elements are derived for Hn+ systems (n=3, 4 and 5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H3+) or triatomics-in-molecules (for H4+ and H5+) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate H2(v′=0,j′=0)+H2+(v,j=0) collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H2+ are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H2+ reactant, and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, are discussed in terms of the long range behaviour of the interaction potential which is properly described within the TRIM formalism. PMID:26696058
NASA Astrophysics Data System (ADS)
Sanz-Sanz, Cristina; Aguado, Alfredo; Roncero, Octavio; Naumkin, Fedor
2015-12-01
Analytical derivatives and non-adiabatic coupling matrix elements are derived for H n+ systems (n = 3-5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H 3+ ) or triatomics-in-molecules (for H 4+ and H 5+ ) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate H 2 ( v ' = 0 , j ' = 0 ) + H2 + ( v , j = 0 ) collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H 2+ are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H 2+ reactant and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, is discussed in terms of the long range behaviour of the interaction potential which is properly described within the triatomics-in-molecules formalism.
NASA Astrophysics Data System (ADS)
Zhai, Hua; Zhang, Jialin; Yu, Hongwei
2016-08-01
We study the geometric phase of a uniformly accelerated two-level atom coupled with vacuum fluctuations of electromagnetic fields in the presence of a perfectly reflecting plane. We find that the geometric phase difference between the accelerated and inertial atoms which can be observed by atom interferometry crucially depends on the polarizability of the atom and the distance to the boundary and it can be dramatically manipulated with anisotropically polarizable atoms. In particular, extremely close to the boundary, the phase difference can be increased by two times as compared to the case without any boundary. So, the detectability of the effects associated with acceleration using an atom interferometer can be significantly increased by the presence of a boundary using atoms with anisotropic polarizability.
Takano, Yoshihide; Liou, Kuo-Nan
2010-07-10
We have developed a hit-and-miss Monte Carlo geometric ray-tracing program to compute the scattering phase matrix for concentrically stratified spheres. Using typical refractive indices for water and aerosols in the calculations, numerous rainbow features appear in the phase matrix that deviate from the results calculated from homogeneous spheres. In the context of geometric ray tracing, rainbows and glory are identified by means of their ray paths, which provide physical explanation for the features produced by the "exact" Lorenz-Mie theory. The computed results for the phase matrix, the single-scattering albedo, and the asymmetry factor for a size parameter of approximately 600 compared closely with those evaluated from the "exact" theory. PMID:20648178
Faraji-Dana, Zahra; Tam, Fred; Chen, J. Jean; Graham, Simon J.
2016-01-01
Echo planar imaging (EPI) suffers from geometric distortions caused by magnetic field inhomogeneities, which can be time-varying as a result of small amounts of head motion that occur over seconds and minutes during fMRI experiments, also known as “dynamic geometric distortion”. Phase Labeling for Additional Coordinate Encoding (PLACE) is a promising technique for geometric distortion correction without reduced temporal resolution and in principle can be used to correct for motion-induced dynamic geometric distortion. PLACE requires at least two EPI images of the same anatomy that are ideally acquired with no variation in the magnetic field inhomogeneities. However, head motion and lung ventilation during the respiratory cycle can cause changes in magnetic field inhomogeneities within the EPI pair used for PLACE. In this work, we exploited dynamic off-resonance in k-space (DORK) and averaging to correct the within EPI pair magnetic field inhomogeneities; and hence proposed a combined technique (DORK+PLACE+averaging) to mitigate dynamic geometric distortion in EPI-based fMRI while preserving the temporal resolution. The performance of the combined DORK, PLACE and averaging technique was characterized through several imaging experiments involving test phantoms and six healthy adult volunteers. Phantom data illustrate reduced temporal standard deviation of fMRI signal intensities after use of combined dynamic PLACE, DORK and averaging compared to the standard processing and static geometric distortion correction. The combined technique also substantially improved the temporal standard deviation and activation maps obtained from human fMRI data in comparison to the results obtained by standard processing and static geometric distortion correction, highlighting the utility of the approach. PMID:27258194
Accurate potential energy functions, non-adiabatic and spin-orbit couplings in the ZnH(+) system.
Liang, Guiying; Liu, Xiaoting; Zhang, Xiaomei; Xu, Haifeng; Yan, Bing
2016-03-01
A high-level ab initio calculation on the ZnH(+) cation has been carried out with the multi-reference configuration interaction method plus Davison correction (MRCI+Q). The scalar relativistic effect is included by using the Douglas-Kroll-Hess (DKH) method. The calculated potential energy curves (PECs) of the 7 Λ-S states are associated with the dissociation limits of Zn(+)((2)Sg)+H((2)Sg), Zn((1)Sg)+H(+)((1)Sg), and Zn(+)((2)Pu)+H((2)Sg), respectively (The Λ-S state is labeled as (2S+1)Λ, in which Λ is the quantum number for the projection along the internuclear axis of the total electronic orbital angular momentum and S is the total electron spin). The spectroscopic constants of the bound states are determined and in good agreement with the available theoretical and experimental results. The permanent dipole moments (PDMs) of Λ-S states and the spin-orbit (SO) matrix elements between Λ-S states are also computed. The results show that the abrupt changes of the PDMs and SO matrix elements come into being for the reason of the avoided crossing between the states with the same symmetry. In addition, the non-adiabatic couplings matrix elements between Λ-S states are also evaluated. Finally, the spin-orbit couplings (SOCs) for the low-lying states are considered with Breit-Pauli operator. The SOC effect makes the 7 Λ-S states of the ZnH(+) cation split into 12 Ω states (Ω=Λ+Sz, in which Sz is projection of the total electron spin S along the internuclear Z-axis). For the (3)0(+) state, the two energy minima exhibit in the potential, which could be attributed to the formation of the new avoided crossing point. The transition dipole moments (TDMs), Franck-Condon factors, and the radiative lifetimes of the selected transitions (2)0(+)-X0(+), (3)0(+)-X0(+), (2)1-X0(+) and (3)1-X0(+) have been reported. PMID:26637984
Accurate potential energy functions, non-adiabatic and spin-orbit couplings in the ZnH+ system
NASA Astrophysics Data System (ADS)
Liang, Guiying; Liu, Xiaoting; Zhang, Xiaomei; Xu, Haifeng; Yan, Bing
2016-03-01
A high-level ab initio calculation on the ZnH+ cation has been carried out with the multi-reference configuration interaction method plus Davison correction (MRCI + Q). The scalar relativistic effect is included by using the Douglas-Kroll-Hess (DKH) method. The calculated potential energy curves (PECs) of the 7 Λ-S states are associated with the dissociation limits of Zn+(2Sg) + H(2Sg), Zn(1Sg) + H+(1Sg), and Zn+(2Pu) + H(2Sg), respectively (The Λ-S state is labeled as 2S + 1Λ, in which Λ is the quantum number for the projection along the internuclear axis of the total electronic orbital angular momentum and S is the total electron spin). The spectroscopic constants of the bound states are determined and in good agreement with the available theoretical and experimental results. The permanent dipole moments (PDMs) of Λ-S states and the spin-orbit (SO) matrix elements between Λ-S states are also computed. The results show that the abrupt changes of the PDMs and SO matrix elements come into being for the reason of the avoided crossing between the states with the same symmetry. In addition, the non-adiabatic couplings matrix elements between Λ-S states are also evaluated. Finally, the spin-orbit couplings (SOCs) for the low-lying states are considered with Breit-Pauli operator. The SOC effect makes the 7 Λ-S states of the ZnH+ cation split into 12 Ω states (Ω = Λ + Sz, in which Sz is projection of the total electron spin S along the internuclear Z-axis). For the (3)0+ state, the two energy minima exhibit in the potential, which could be attributed to the formation of the new avoided crossing point. The transition dipole moments (TDMs), Franck-Condon factors, and the radiative lifetimes of the selected transitions (2)0+-X0+, (3)0+-X0+, (2)1-X0+ and (3)1-X0+ have been reported.
Experimental realization of non-abelian geometric gates with a superconducting three-level system
NASA Astrophysics Data System (ADS)
Abdumalikov, Abdufarrukh; Fink, J. M.; Juliusson, K.; Pechal, M.; Berger, S.; Wallraff, A.; Filipp, S.
2013-03-01
Geometric gates hold promise to provide the building blocks for robust quantum computation. In our experiments, we use a superconducting three-level system (transmon) to realize non-adiabatic non-abelian geometric gates. As computational basis we choose the ground and second excited states, while the first excited state acts as an ancilla state. The gates are realized by applying two resonant drives between the transmon levels. During the geometric gate ration of the amplitudes of the two drive tone is kept constant. Different gates are obtained for different ratio of the drive tones. We implement a Hadamard, a NOT and a phase gates with the fidelities of 95 % , 98 % , and 97 % as determined by full process tomography and maximum likelihood methods. We explicitly show the non-abelian nature of gates by applying two non-commuting gates in alternating order. The demonstrated holonomic gates are not exclusive to superconducting quantum devices, but can also be applied to other three level systems with similar energy level structure.
Jian Liu and Hong Qin
2012-08-22
The reformulation of our analysis on the geometric phase of the gyromotion [J. Liu and H. Qin, Phys. Plasmas 18, 072505 (2011)] in terms of spatial angles presented in the comment by Brizard and Guillebon is interesting and correct. The subtlety of whether the adiabatic term associated with the long term average of the variation of pitch angle completely disappears after the gyrophase average is related to where valid approximations are applied. But it has no impact on the main conclusions.
NASA Astrophysics Data System (ADS)
Kobayashi, S.; Mitsuda, S.; Prokes, K.
2001-01-01
Low-temperature magnetic phase transitions of the geometrically frustrated isosceles triangular Ising antiferromagnet CoNb2O6 have been investigated by means of neutron diffraction down to T=0.2 K under applied fields up to H∥c=4.4 kOe. Below T~0.6 K, the relaxation time of the system becomes extremely long compared with our observation time, being responsible for all the anomalous low-temperature magnetic properties observed in the bulk measurements [T. Hanawa et al., J. Phys. Soc. Jpn. 63, 2706 (1994)]. In addition to confirmation of the triple point where the antiferromagnetic, field-induced ferrimagnetic, and incommensurate phases meet together in the H∥c-T magnetic phase diagram, we also found various ordered phases that are field induced between the ferrimagnetic and saturated paramagnetic phases.
Geometric Phase, Zeeman, and Optical Effects in the Excitation of Lead Fluoride and Kryptonite
NASA Astrophysics Data System (ADS)
Rupasinghe, Priyanka Milinda
2011-12-01
This dissertation is motivated by two major challenges in modern Physics. One is related to precession measurement and other is related to atmospheric science. The amount of CP violation (equivalently time reversal (T) symmetry violation) that occurs in the Standard Model, the most successful theory in the particle physics today, is not sufficient to explain why we live in a matter (rather than anti-matter) dominated universe. A measurable electric dipole moment of the electron (e-EDM) proportional to its spin may help to unravel this matter anti-matter mystery and could point the way to physics beyond the Standard Model. As an e-EDM probe, both cold molecular trap and molecular beam techniques have been proposed. In this thesis we show that the geometric phase effect limits the viability of a cold molecular trap technique. Specifically we show the molecular trap method can not be employed for PbF until the technology is available to cool down molecules to ultra cold temperatures. This thesis also addresses two major difficulties that need to be overcome in order to carry out a molecular beam e-EDM measurement. One of these difficulties is that background magnetic fields mimic the e-EDM. For this reason, molecules with small magnetic g-factors greatly reduce the background due to this effect. In this dissertation investigation of the Zeeman structure of the PbF molecule including state dependent g-factor measurements are determined through extensive analysis of microwave spectroscopy. The other major difficulty addressed in this thesis is the requirement to create a highly uniform electric field that can be reversed in a precise and consistent manner. Specifically we describe a precise high voltage control and switching system that has been built. Isotopic detection of Krypton has many important applications including archaeological dating beyond that possible using ^{14}C and nuclear activitymonitoring all around the world. It has been shown that laser cooling and
NASA Astrophysics Data System (ADS)
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2014-03-01
Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.
Imai, Hiromitsu; Otsubo, Yuki; Morinaga, Atsuo
2007-07-15
The geometric manipulation of the quantum states of two-level atoms with two laser-controlled resonant {pi} pulses with a relative phase difference was evaluated using a time-domain atom interferometer comprising a cold sodium atom ensemble and two copropagating two-photon Raman pulses. It was verified that the relative phase shift between two states is double the control phase difference and that the rotation around the axis 3 of the Bloch sphere can be controlled by geometric manipulation.
NASA Astrophysics Data System (ADS)
Casana, R.; Ferreira, M. M.; Mouchrek-Santos, V. E.; Silva, Edilberto O.
2015-06-01
We have demonstrated that Lorentz-violating terms stemming from the fermion sector of the SME are able to generate geometrical phases on the wave function of electrons confined in 1-dimensional rings, as well as persistent spin currents, in the total absence of electromagnetic fields. We have explicitly evaluated the eigenenergies and eigenspinors of the electrons modified by the Lorentz-violating terms, using them to calculate the dynamic and the Aharonov-Anandan phases in the sequel. The total phase presents a pattern very similar to the Aharonov-Casher phase accumulated by electrons in rings under the action of the Rashba interaction. Finally, the persistent spin current were carried out and used to impose upper bounds on the Lorentz-violating parameters.
Geometric phase and o-mode blueshift in a chiral anisotropic medium inside a Fabry-Pérot cavity.
Timofeev, Ivan V; Gunyakov, Vladimir A; Sutormin, Vitaly S; Myslivets, Sergey A; Arkhipkin, Vasily G; Vetrov, Stepan Ya; Lee, Wei; Zyryanov, Victor Ya
2015-11-01
Anomalous spectral shift of transmission peaks is observed in a Fabry-Pérot cavity filled with a chiral anisotropic medium. The effective refractive index value resides out of the interval between the ordinary and the extraordinary refractive indices. The spectral shift is explained by contribution of a geometric phase. The problem is solved analytically using the approximate Jones matrix method, numerically using the accurate Berreman method, and geometrically using the generalized Mauguin-Poincaré rolling cone method. The o-mode blueshift is measured for a 4-methoxybenzylidene-4'-n-butylaniline twisted-nematic layer inside the Fabry-Pérot cavity. The twist is electrically induced due to the homeoplanar-twisted configuration transition in an ionic-surfactant-doped liquid crystal layer. Experimental evidence confirms the validity of the theoretical model. PMID:26651714
Cotton, Stephen J; Miller, William H
2016-03-01
In a recent series of papers, it has been illustrated that a symmetrical quasi-classical (SQC) windowing model applied to the Meyer-Miller (MM) classical vibronic Hamiltonian provides an excellent description of a variety of electronically non-adiabatic benchmark model systems for which exact quantum results are available for comparison. In this paper, the SQC/MM approach is used to treat energy transfer dynamics in site-exciton models of light-harvesting complexes, and in particular, the well-known 7-state Fenna-Mathews-Olson (FMO) complex. Again, numerically "exact" results are available for comparison, here via the hierarchical equation of motion (HEOM) approach of Ishizaki and Fleming, and it is seen that the simple SQC/MM approach provides very reasonable agreement with the previous HEOM results. It is noted, however, that unlike most (if not all) simple approaches for treating these systems, because the SQC/MM approach presents a fully atomistic simulation based on classical trajectory simulation, it places no restrictions on the characteristics of the thermal baths coupled to each two-level site, e.g., bath spectral densities (SD) of any analytic functional form may be employed as well as discrete SD determined experimentally or from MD simulation (nor is there any restriction that the baths be harmonic), opening up the possibility of simulating more realistic variations on the basic site-exciton framework for describing the non-adiabatic dynamics of photosynthetic pigment complexes. PMID:26761191
Sinitsyn, Nikolai A
2008-01-01
We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the noncyclic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We also discuss a model, where this correction qualitatively changes the outcome of reaction kinetics.
On a relation of the angular frequency to the Aharonov-Casher geometric phase in a quantum dot
NASA Astrophysics Data System (ADS)
Barboza, P. M. T.; Bakke, K.
2016-09-01
By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov-Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov-Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.
A composite phase diagram of structure H hydrates using Schreinemakers' geometric approach
Mehta, A.P.; Makogon, T.Y.; Burruss, R.C.; Wendlandt, R.F.; Sloan, E.D.
1996-01-01
A composite phase diagram is presented for Structure H (sH) clathrate hydrates. In this work, we derived the reactions occurring among the various phases along each four-phase (Ice/Liquid water, liquid hydrocarbon, vapor, and hydrate) equilibrium line. A powerful method (though seldom used in chemical engineering) for multicomponent equilibria developed by Schreinemakers is applied to determine the relative location of all quadruple (four-phase) lines emanating from three quintuple (five-phase) points. Experimental evidence validating the approximate phase diagram is also provided. The use of Schreinemakers' rules for the development of the phase diagram is novel for hydrates, but these rules may be extended to resolve the phase space of other more complex systems commonly encountered in chemical engineering.