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Bulletin of the American Physical Society

Shortcuts to adiabaticity in classical and quantum processes for scale-invariant driving

Sebastian Deffner, Christopher Jarzynski, Adolfo del Campo

Published Mar 3, 2014• 0 citations
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Shortcuts to Adiabaticity in Quantum Many-Body Systems

Adolfo del Campo

Bulletin of the American Physical Society•Mar 3, 2015•0 citations
Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity . In one approach, a counterdiabatic quantum Hamiltonian, Ĥ CD, is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian, H CD, ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions, or translations of the system. Here we investigate an example of a non-scale-invariant system, a tilted piston . We solve exactly for the classical counterdiabatic Hamiltonian, H CD ( q, p, t ), which we then quantize to obtain a Hermitian operator, Ĥ CD ( t ). Using numerical simulations, we find that Ĥ CD effectively suppresses nonadiabatic excitations under rapid driving. These results offer a proof of principle, beyond the special case of scale-invariant driving, that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.
It is known that the dynamics and geometric phase of a quantum system can be simulated by classical coupled oscillators using 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 shortcuts to adiabaticity, which can quickly achieve the adiabatic effect through a non-adiabatic process. By mapping quantum systems by classical oscillators, two schemes, Berry’s “transitionless quantum driving” and the Lewis−Riesenfeld invariant method, are simulated by a corresponding transitionless classical driving method, which keeps adiabatic phase trajectories and acquires 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 quantum shortcuts-to-adiabaticity methods.