Engineering quantum Mpemba effect by Liouvillian skin effect

TL;DR

This paper introduces a new method to engineer the quantum Mpemba effect using the Liouvillian skin effect in open quantum systems, simplifying initial state preparation and revealing new phenomena related to state relaxation.

Contribution

It demonstrates how the Liouvillian skin effect can be used to realize the quantum Mpemba effect without complex initial-state design, and uncovers a new type of QME involving off-diagonal correlations.

Findings

QME can be realized via spatial profile of initial states in LSE systems.

Distinct relaxation behaviors (algebraic vs exponential) depend on initial state localization.

New QME phenomenon with two crossings in Hilbert-Schmidt distance when off-diagonal correlations are present.

Abstract

We propose a novel approach to engineer the quantum Mpemba effect (QME)-wherein an initial state farther from the steaty state relaxes faster than a closer one-by the Liouvillian skin effect (LSE) in open quantum systems. We show that, in the open quantum chain with LSE, QME can be easily realized by considering only the spatial profile of initial states, since the initial states localized on the left or right edges experience distinctive relaxation process (algebraic or exponential decay). This approach circumvents the necessity of careful initial-state design and fine-tuning of control parameter. Moreover, when the initial correlation matrix contains off-diagonal elements, we uncover a new kind of QME which manifest as two crossings in the Hilbert-Schmidt distance at different times. This work unveils the deep connection between QME and LSE, and provides a physically intuitive understanding of QME and straightforward pathway for the initial state preparation thereby enabling readily accessible experimental preparation.