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arXiv:1208.5650 · Physical Review A

Acceleration of adiabatic transport of interacting particles and rapid manipulations of a dilute Bose gas in the ground state

Shumpei Masuda

Published Dec 19, 2012• 38 citations
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Abstract

We show a method to accelerate quantum adiabatic transport of identical spinless particles interacting with each other by developing the preceding fast-forward scaling theory formed for one-particle systems [Masuda and Nakamura, Proc. R. Soc. A 466, 1135 (2010)]. We derive a driving potential which accelerates adiabatic dynamics of quantum systems composed of identical particles in order to obtain the final adiabatic states in any desired short time. We also exhibit an ideal rapid manipulation of dilute Bose gas in the ground state without energy excitation by using the fast-forward scaling theory.

DOI
10.1103/physreva.86.063624

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We show a method to accelerate quantum adiabatic transport of identical spinless particles interacting with each other by developing the preceding fast-forward scaling theory formed for one-particle systems [Masuda and Nakamura, Proc. R. Soc. A 466, 1135 (2010)]. We derive a driving potential which accelerates adiabatic dynamics of quantum systems composed of identical particles in order to obtain the final adiabatic states in any desired short time. We also exhibit an ideal rapid manipulation of dilute Bose gas in the ground state without energy excitation by using the fast-forward scaling theory.
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 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 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.
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.
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.
Quantum information processing requires fast manipulations of quantum systems in order to overcome dissipative effects. We propose a method to accelerate quantum dynamics and obtain a target state in a shorter time relative to unmodified dynamics, and apply the theory to a system consisting of two linearly coupled qubits. We extend the technique to accelerate quantum adiabatic evolution in order to rapidly generate a desired target state, thereby realizing a shortcut to adiabaticity. Further, we address experimental limitations to the rate of change of control parameters for quantum devices which often limit one's ability to generate a desired target state with high fidelity. We show that an initial state following decelerated dynamics can reach a target state while varying control parameters more slowly, enabling more experimentally feasible driving schemes.