Classical and Quantum Shortcuts to Adiabaticity in a Tilted Piston.

Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian, ĤCD, is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian, HCD, 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, HCD(q, p, t), which we then quantize to obtain a Hermitian operator, ĤCD(t). Using numerical simulations, we find that ĤCD 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.