Accuracy of the adiabatic-impulse approximation for closed and open quantum systems

TL;DR

This paper evaluates the accuracy of the adiabatic-impulse approximation (AIA) in quantum systems, revealing its strengths and limitations for different driving speeds, and proposing a modified AIA that improves performance.

Contribution

It systematically assesses the AIA's accuracy in closed and open quantum systems and introduces a modified AIA crossing the small gap region twice for better results.

Findings

AIA outperforms adiabatic approximation for fast protocols.

AIA performs worse than adiabatic approximation for slow protocols.

A modified AIA crossing the small gap twice can outperform the standard AIA.

Abstract

We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states, when driven through a region of small gap. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead here, we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times/fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times/slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counter-intuitive modification consists in crossing twice the region of small gap. Our findings are illustrated by several examples of driven closed and open quantum systems.