Out-of-equilibrium evolution of kinetically constrained many-body quantum systems under purely dissipative dynamics

TL;DR

This paper investigates how quantum many-body systems with purely dissipative dynamics relax over time, revealing that quantum coherence can significantly slow relaxation compared to classical models, especially in kinetically constrained systems like Rydberg gases.

Contribution

It introduces a framework to compare quantum and classical dissipative relaxation, highlighting the impact of quantum coherence on slowing dynamics in kinetically constrained models.

Findings

Quantum relaxation can be orders of magnitude slower than classical.

Quantum coherences significantly influence the relaxation process.

Rydberg gases under EIT conditions serve as physical realizations of quantum KCMs.

Abstract

We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.