Classical and quantum shortcuts to adiabaticity in a tilted piston

TL;DR

This paper demonstrates that classical counterdiabatic Hamiltonians can be quantized to create effective shortcuts to adiabaticity in quantum systems, extending beyond previously studied scale-invariant cases, with a focus on a tilted piston.

Contribution

The authors derive and quantize a classical counterdiabatic Hamiltonian for a non-scale-invariant tilted piston, showing it effectively suppresses non-adiabatic excitations in quantum dynamics.

Findings

Classical counterdiabatic Hamiltonian for a tilted piston is exactly solved.

Quantized Hamiltonian effectively suppresses non-adiabatic excitations.

Extension of shortcuts to adiabaticity beyond scale-invariant systems.

Abstract

Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian $\hat H_{CD}$ 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 $\hat H_{CD}(t)$. Using numerical simulations, we find that $\hat H_{CD}$ effectively suppresses non-adiabatic 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.