Excess work in counterdiabatic driving

TL;DR

This paper investigates the energetic cost of counterdiabatic driving in quantum systems by analyzing excess work, proposing a new interpretation to quantify energy expenditure despite the traditional zero excess work result.

Contribution

It introduces a novel interpretation of the counterdiabatic Hamiltonian parameters to quantify energy costs via excess work, addressing the challenge of zero excess work in standard analysis.

Findings

Excess work can quantify energy transitions in counterdiabatic driving.

A new parameter interpretation yields non-zero excess work for cost assessment.

Illustrated with the Landau-Zener model.

Abstract

Many years have passed since the conception of the quintessential method of shortcut to adiabaticity known as counterdiabatic driving (or transitionless quantum driving). Yet, this method appears to be energetically cost-free and thus continually challenges the task of quantifying the amount of energy it demands to be accomplished. This paper proposes that the energy cost of controlling a closed quantum system using the counterdiabatic method can also be assessed using the instantaneous excess work during the process and related quantities, as the time-averaged excess work. Starting from the Mandelstam-Tamm bound for driven dynamics, we have shown that the speed-up of counterdiabatic driving is linked with the spreading of energy between the eigenstates of the total Hamiltonian, which is necessarily accompanied by transitions between these eigenstates. Nonetheless, although excess work can be used to quantify energetically these transitions, it is well known that the excess work is zero throughout the entire process under counterdiabatic driving. To recover the excess work as an energetic cost quantifier for counterdiabatic driving, we will propose a different interpretation of the parameters of the counterdiabatic Hamiltonian, leading to an excess work different from zero. We have illustrated our findings with the Landau-Zener model.