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arXiv:1004.4108

Fast-forward of quantum adiabatic dynamics in electro-magnetic field

Shumpei Masuda, Katsuhiro Nakamura

Published Apr 23, 2010• 2 citations
arXivHTMLPDF

Abstract

We show a method to accelerate quantum adiabatic dynamics of wavefunctions under electro-magnetic field by developing the previous theory (Masuda & Nakamura 2008 and 2010). Firstly we investigate the orbital dynamics of a charged particle. We derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states except for the spatially uniform phase such as the adiabatic phase in any desired short time. Fast-forward of adiabatic squeezing and transport in the electro-magnetic field is exhibited. Secondly we investigate spin dynamics under the magnetic field, showing the fast-forward of adiabatic spin inversion and of adiabatic dynamics in Landau-Zener model. The connection of the present framework with Kato-Berry's transitionless quantum driving is elucidated in Appendix.

DOI
10.48550/arxiv.1004.4108

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We show a method to accelerate quantum adiabatic dynamics of wavefunctions under electro-magnetic field by developing the previous theory (Masuda & Nakamura 2008 and 2010). Firstly we investigate the orbital dynamics of a charged particle. We derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states except for the spatially uniform phase such as the adiabatic phase in any desired short time. Fast-forward of adiabatic squeezing and transport in the electro-magnetic field is exhibited. Secondly we investigate spin dynamics under the magnetic field, showing the fast-forward of adiabatic spin inversion and of adiabatic dynamics in Landau-Zener model. The connection of the present framework with Kato-Berry's transitionless quantum driving is elucidated in Appendix.
We show a method to accelerate quantum adiabatic dynamics of wave functions under electromagnetic field (EMF) by developing the preceding theory [Masuda and Nakamura, Proc. R. Soc. London Ser. A 466, 1135 (2010)]. Treating the orbital dynamics of a charged particle in EMF, we derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states in any desired short time. The scheme is consolidated by describing a way to overcome possible singularities in both the additional phase and driving potential due to nodes proper to wave functions under EMF. As explicit examples, we exhibit the fast forward of adiabatic squeezing and transport of excited Landau states with nonzero angular momentum, obtaining the result consistent with the transitionless quantum driving applied to the orbital dynamics in EMF.
We propose a method to accelerate adiabatic dynamics of wave functions (WFs) in quantum mechanics to obtain a final adiabatic state except for the spatially uniform phase in any desired short time. In our previous work, acceleration of the dynamics of WFs was shown to obtain the final state in any short time by applying driving potential. We develop the previous theory of fast-forward to derive a driving potential for the fast-forward of adiabatic dynamics. A typical example is the fast-forward of adiabatic transport of a WF, which is the ideal transport in the sense that a stationary WF is transported to an aimed position in any desired short time without leaving any disturbance at the final time of the fast-forward. As other important examples, we show accelerated manipulations of WFs, such as their splitting and squeezing. The theory is also applicable to macroscopic quantum mechanics described by the nonlinear Schrödinger equation.
We study a scheme of fast-forward adiabatic quantum dynamics of a (2 + 1) Dirac particle. This scheme was originally proposed by Masuda and Nakamura. In this scheme, we include the adiabatic parameter that maintains the adiabatic motion of the particle and fast forward its motion by introducing a time scaling parameter. The fast forward adiabatic state is obtained by determining the regularization term and driving potential. We introduce the proposed method to the system with the Dirac particle using a (2 + 1) dimensiontime- dependent Dirac equation and obtain the regularization term, the driving scalar potential VFF and the driving vector potential AFF . By tuning the driving electric field, this method can accelerate the adiabatic dynamics of an electron as a Dirac particle trapped in the ground state in the plane xy and an electric field in the x direction and a constant magnetic field in the y direction. This acceleration will preserve the ground state of the wave function from the initial time to the final time.
Abstract We discussed a method to accelerate an adiabatic quantum dynamics of XY spin model by using the fast-forward method proposed by Masuda and Nakamura. The Accelerated scheme is constructed by adding the driving Hamiltonian to the original Hamiltonian and speeding it up with a large time-scaling factor and an adiabatic parameter that realizes adiabatic quantum dynamics in a shortened time. Accelerated adiabatic dynamics start by assuming the candidate of driving Hamiltonian consists of the pair-wise exchange interaction and magnetic field. The driving Hamiltonian terms multiplied by the velocity function together with the original Hamiltonian give fast-forward driving for adiabatic states. We apply our method to XY spin model by considering three spin systems on the Kagome lattice. In this model, we obtained the XY pair-wise exchange interaction of nearest neighbors and next-nearest neighbors should be added to the original Hamiltonian as a driving interaction to accelerate the adiabatic motion. This pair-wise driving interaction in the fast-forward scheme guarantees the complete fidelity of accelerated states.
This research examines the application of the fast forward method to single spin with Rabi frequency. In this study, the electron spin dynamics are examined by accelerating adiabatic quantum dynamics. Through the concept of adiabatic will be obtained unchanged state of the system, at the beginning and end of the evolution of the system. This study aims to obtain an additional Hamiltonian on the concept of accelerated adiabatic quantum dynamics on single spin. The method used is the fast forward method developed by Masuda and Nakamura. The result of this research is to obtain the additional Hamiltonian “equation 54” and the driving magnetic field through the fast forward method “equation 56”. The fast forward method is applied by first obtaining the eigenvalues of the Hamiltonian system. Furthermore, by reviewing the lowest energy state (ground state). It is concluded that this study obtained an additional Hamiltonian term with a driving magnetic field that ensures that a single spin can move from the initial state to the final state in a short time, while maintaining the characteristics of each energy level in the system.
This research examines the application of the fast forward method to single spin with Rabi frequency. In this study, the electron spin dynamics are examined by accelerating adiabatic quantum dynamics. Through the concept of adiabatic will be obtained unchanged state of the system, at the beginning and end of the evolution of the system. This study aims to obtain an additional Hamiltonian on the concept of accelerated adiabatic quantum dynamics on single spin. The method used is the fast forward method developed by Masuda and Nakamura. The result of this research is to obtain the additional Hamiltonian “equation 54” and the driving magnetic field through the fast forward method “equation 56”. The fast forward method is applied by first obtaining the eigenvalues of the Hamiltonian system. Furthermore, by reviewing the lowest energy state (ground state). It is concluded that this study obtained an additional Hamiltonian term with a driving magnetic field that ensures that a single spin can move from the initial state to the final state in a short time, while maintaining the characteristics of each energy level in the system.