Optimal Shortcuts to Adiabaticity for a Quantum Piston

TL;DR

This paper develops optimal control strategies to achieve rapid adiabatic-like expansion of a quantum piston, improving efficiency and providing insights into thermodynamics and quantum state manipulation.

Contribution

It introduces a method to design minimum-time adiabatic-like paths for quantum pistons under realistic constraints, surpassing previous inverse engineering approaches.

Findings

Minimum expansion time calculated under experimental constraints

Re-derivation of the upper bound for refrigerator cooling rate

Connection to quantum microscope applications

Abstract

In this paper we use optimal control to design minimum-time adiabatic-like paths for the expansion of a quantum piston. Under realistic experimental constraints, we calculate the minimum expansion time and compare it with that obtained from a state of the art inverse engineering method. We use this result to rederive the known upper bound for the cooling rate of a refrigerator, which provides a quantitative description for the unattainability of absolute zero, the third law of thermodynamics. We finally point out the relation of the present work to the fast adiabatic-like expansion of an accordion optical lattice, a system which can be used to magnify the initial quantum state (quantum microscope).