Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect

TL;DR

This paper explores a non-Hermitian quantum model with non-reciprocal hoppings, revealing a Liouvillian skin effect and accelerated relaxation, while highlighting gaps in current theoretical understanding of quantum relaxation mechanisms.

Contribution

It introduces a non-Hermitian model exhibiting Liouvillian skin effect and accelerated relaxation, and proposes a method to realize it in atomic systems, advancing quantum relaxation theory.

Findings

Liouvillian skin effect confirmed in the model

Gradient hopping accelerates relaxation time

Discrepancy with existing Liouvillian skin effect theories

Abstract

We investigate a non-Hermitian model featuring non-reciprocal gradient hoppings. Through an in-depth analysis of the Liouvillian spectrum and dynamics, we confirm the emergence of the Liouvillian skin effect resulting from the non-reciprocal nature of hoppings in this model. Furthermore, we observe that the presence of gradient hopping strength leads to an accelerated relaxation time for the system. Through numerical investigations of the Liouvillian gap, relaxation time, and steady-state localization length, we discover that the relaxation time in this model cannot be explained by the currently established relationship associated with the Liouvillian skin effect. This discrepancy highlights the need for further exploration and theoretical advancements to fully comprehend the intricate mechanisms underlying quantum relaxation processes. Motivated by these findings, we propose a theoretical approach to realize this non-Hermitian model in an atomic system with a sideband structure by employing adiabatic elimination technique. These results contribute to our deeper comprehension of quantum relaxation dynamics and provide theoretical backing for the development of techniques aimed at controlling quantum relaxation processes.