Not quite free shortcuts to adiabaticity

TL;DR

This paper investigates the fundamental limitations of shortcuts to adiabaticity in quantum systems, highlighting how quantum fluctuations impose a cost and affect the efficiency of quantum heat engines.

Contribution

It introduces a theoretical framework to quantify the cost of implementing shortcuts to adiabaticity due to quantum fluctuations, extending understanding of their practical limits.

Findings

Quantum fluctuations cause deviations from adiabatic paths.

There is an inherent energy cost in using STA, even at zero temperature.

A consistency condition for classical approximation validity is derived.

Abstract

Given the increasing use of shotcuts to adiabaticity (STA) to optimize power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from the adiabatic path. This not only induces transitions to unwanted final states but also changes the system energy, so that using the STA has a definite cost in terms of conventional work definitions. This may be the ultimate cost of an adiabatic shortcut, in the sense that it is present even for a frictionless, zero temperature driving. We estimate the effect, to lowest nontrivial order in the derivatives of the time-dependent frequency, on a parametric harmonic oscillator, thus providing a consistency condition for the validity of the classical approximation.