AUTHOR=Liu Yang , Zhang Y. N. , Liu H. D. , Sun H. Y. 

TITLE=Simulation of quantum shortcuts to adiabaticity by classical oscillators

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1090973

DOI=10.3389/fphy.2022.1090973

ISSN=2296-424X

ABSTRACT=It is known that the dynamics and geometric phase of a quantum system can be simulated by the classical coupled oscillators in the quantum-classical mapping method without loss of physics. In this work, we show that this method can also be used to simulate the schemes of quantum shortcut to adiabaticity which can quickly achieve the adiabatic effect through a non-adiabatic process. By mapping quantum systems by classical oscillators, the two schemes, Berry's ``transitionless quantum driving"  and the Lewis-Riesenfeld invariant method, are simulated by a corresponding transitionless classical driving method which keeps the adiabatic phase trajectories and acquires the Hannay's angle and the classical Lewis-Riesenfeld invariant method by manipulating the configurations of classical coupled oscillators. The classical shortcuts to adiabaticity for the two coupled classical oscillators, which is the classical version of a spin-1/2 in a magnetic field, is employed to illustrate our results and compared with the quantum shortcuts-to-adiabaticity methods.