Classical and Quantum Shortcuts to Adiabaticity in a Tilted Piston

Area of Science:

• Quantum mechanics
• Classical mechanics
• Statistical physics

Background:

• Adiabatic quantum state evolution is typically slow.
• Shortcuts to adiabaticity accelerate this process.
• Counterdiabatic Hamiltonians suppress nonadiabatic excitations.

Purpose of the Study:

• Investigate shortcuts to adiabaticity for non-scale-invariant systems.
• Construct and quantize a classical counterdiabatic Hamiltonian for a tilted piston.
• Verify the effectiveness of the quantum counterdiabatic Hamiltonian in suppressing excitations.

Main Methods:

• Exact solution for the classical counterdiabatic Hamiltonian.
• Quantization of the classical Hamiltonian to a Hermitian operator.
• Numerical simulations to assess the suppression of nonadiabatic excitations.

Main Results:

• The classical counterdiabatic Hamiltonian was exactly solved for a tilted piston.
• The quantized Hamiltonian effectively suppressed nonadiabatic excitations under rapid driving.
• Demonstrated a proof of principle for constructing quantum shortcuts from classical counterparts.

Conclusions:

• Quantum shortcuts to adiabaticity can be successfully constructed from classical counterparts for non-scale-invariant systems.
• The developed counterdiabatic Hamiltonian provides an effective method for accelerating quantum state evolution.
• This work extends the applicability of shortcuts to adiabaticity beyond scale-invariant systems.