Shortcuts to adiabaticity from linear response theory

TL;DR

This paper introduces a method to find shortcuts to adiabaticity using linear response theory, enabling finite-time processes that mimic slow adiabatic transformations in quantum systems.

Contribution

It develops a linear response-based framework to identify shortcuts to adiabaticity, providing explicit expressions for excess work and protocols for specific quantum systems.

Findings

Shortcuts correspond to zeros of excess work in response functions.

Explicit protocols for quantum parametric oscillator and spin-1/2 systems.

Degenerate family of protocols for very short driving times.

Abstract

A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. With the help of phenomenological response functions a simple expression for the excess work is found -- quantifying the nonequilibrium excitations. For two specific examples, the quantum parametric oscillator and the spin-1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. Finally, we propose a degenerate family of protocols, which facilitate shortcuts to adiabaticity for specific and very short driving times.