Dynamical aspects of steady-state subradiance: Detailed balance and its breakdown

TL;DR

This paper explores how the dynamics of a dissipative quantum system, specifically a bad-cavity laser, can be described by a Markov chain, revealing a phase transition characterized by detailed balance and time asymmetry.

Contribution

It establishes a connection between dissipative phase transitions in a quantum system and the properties of an underlying Markov chain, highlighting detailed balance breakdown.

Findings

In one phase, the Markov chain approaches detailed balance as atom number increases.

In the other phase, time-asymmetric probability currents emerge, indicating detailed balance breakdown.

The breakdown correlates with observable self-pulsing in the cavity light output.

Abstract

The dynamics of dissipative many-body quantum systems sometimes admit an emergent classical description in terms of a Markov chain even though the corresponding state space contains highly entangled states. In particular, a bad-cavity laser is a paradigm system whose dynamics can be formulated as a Markov chain in a two-dimensional state space spanned by collective angular momentum states. In this article, we investigate the connection between a dissipative phase transition that occurs in the subradiant regime of this system in the large atom number limit, and the properties of the underlying Markov chain. In one of the phases, the Markov chain approaches the detailed-balance condition with increasing atom number $N$ and hence becomes effectively time-reversible. This is caused by a collective atomic emission process that effectively reduces the Markov chain to one dimension. In the other phase, we find the emergence of time-asymmetric probability currents in the two-dimensional state space that signals a breakdown of detailed balance. This is accompanied by a macroscopic internal entropy production rate in the Markov chain that scales extensively with the atom number $N$. An observable consequence of the probability currents is a self-pulsing of the cavity light output in this phase, which can be detected as an anti-correlation dip in the intensity correlation function.