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New Journal of Physics

How to drive a Dirac system fast and safe

Juan Gonzalo Muga, Miguel Angel Otero Simón, Ander Tobalina

Published Feb 1, 2016• 7 citations
Publisher

Abstract

Abstract A recent article (Deffner New J. Phys. 18 012001 ) discusses how to speed up systems governed by the (1 + 1)-dimensional Dirac equation so that the ideal adiabatic dynamics driven by a reference Hamiltonian is exactly implemented with a different Hamiltonian. The central idea is to apply a particular version of ‘shortcuts to adiabaticity’, namely the ‘fast forward approach’, to the Dirac equation. A broad range of ‘Dirac systems’ may be driven fast and safe using this and related techniques.

DOI
10.1088/1367-2630/18/2/021005

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Abstract A recent article (Deffner New J. Phys. 18 012001 ) discusses how to speed up systems governed by the (1 + 1)-dimensional Dirac equation so that the ideal adiabatic dynamics driven by a reference Hamiltonian is exactly implemented with a different Hamiltonian. The central idea is to apply a particular version of ‘shortcuts to adiabaticity’, namely the ‘fast forward approach’, to the Dirac equation. A broad range of ‘Dirac systems’ may be driven fast and safe using this and related techniques.
Achieving effectively adiabatic dynamics in finite time is a ubiquitous goal in virtually all areas of modern physics. So-called shortcuts to adiabaticity refer to a set of methods and techniques that allow us to produce in a short time the same final state that would result from an adiabatic, infinitely slow process. In this paper we generalize one of these methods—the fast-forward technique—to driven Dirac dynamics. As our main result we find that shortcuts to adiabaticity for the (1+1)(1+1)(1+1)-dimensional Dirac equation are facilitated by a combination of both scalar and pseudoscalar potentials. Our findings are illustrated for two analytically solvable examples, namely charged particles driven in spatially homogeneous and linear vector fields.
Achieving effectively adiabatic dynamics in finite time is a ubiquitous goal in virtually all areas of modern physics. So-called shortcuts to adiabaticity refer to a set of methods and techniques that allow us to produce in a short time the same final state that would result from an adiabatic, infinitely slow process. In this paper we generalize one of these methods—the fast-forward technique—to driven Dirac dynamics. As our main result we find that shortcuts to adiabaticity for the -dimensional Dirac equation are facilitated by a combination of both scalar and pseudoscalar potentials. Our findings are illustrated for two analytically solvable examples, namely charged particles driven in spatially homogeneous and linear vector fields.
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 discuss a method of controlling Dirac dynamics in (2+1)-dimensions using adiabatic fast-forward method proposed by Masuda-Nakamura. Due to infinitely large amount of time of adiabaticity, we have to use an infinitely large scaling factor to shorten the time interval. Thus, we need a regularization to remove this infinity. Our strategy is analogue to adiabatic fast-forward of Schrodinger equation. That is using an auxiliary Hamiltonian but now we use two phase factors applied to the components of spinor. We applied to a case where a system is controlled by uniform magnetic field.
Abstract Shortcuts to adiabaticity guide given systems to final destinations of adiabatic control via fast tracks. Various methods have been proposed as shortcuts to adiabaticity. The basic theory of shortcuts to adiabaticity was established in the 2010s, but it has still been developing and many fundamental findings have been reported. In this topical review, we give a pedagogical introduction to the theory of shortcuts to adiabaticity and revisit relations between different methods. Some versatile approximations in counterdiabatic driving, which is one of the methods of shortcuts to adiabaticity, will be explained in detail. We also summarize the recent progress in studies of shortcuts to adiabaticity.
The ``fast-forward''approach by Masuda and Nakamura generates driving potentials to accelerate slow quantum adiabatic dynamics. First we present a streamlined version of the formalism that produces the main results in a few steps. Then we show the connection between this approach and inverse engineering based on Lewis-Riesenfeld invariants. We identify in this manner applications in which the engineered potential does not depend on the initial state. Finally we discuss more general applications exemplified by wave splitting processes.