Classical and quantum shortcuts to adiabaticity in a tilted piston

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.

13 pages, 7 figures

References in corpus (4)

• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Shortcut to adiabaticity for an interacting Bose-Einstein condensate
• Fast optimal transition between two equilibrium states

Cited by in corpus (13)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Trade-off between speed and cost in shortcuts to adiabaticity
• Shortcuts to adiabaticity using flow fields
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Fast forward to the classical adiabatic invariant
• Hamiltonian engineering for adiabatic quantum computation: Lessons from shortcuts to adiabaticity
• Invariant-based inverse engineering of crane control parameters
• Harnessing Fluctuations in Thermodynamic Computing via Time-Reversal Symmetries
• Shortcuts in stochastic systems and control of biophysical processes
• Shortcuts to adiabaticity applied to nonequilibrium entropy production: An information geometry viewpoint
• Time-rescaling of Dirac dynamics: shortcuts to adiabaticity in ion traps and Weyl semimetals
• Environment-Assisted Shortcuts to Adiabaticity