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, 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.