On the generality of symmetry breaking and dissipative freezing in quantum trajectories

TL;DR

This paper demonstrates that symmetry breaking and dissipative freezing are general phenomena in open quantum systems with strong symmetry, linking spectral properties of the Liouvillian to the dynamics of quantum trajectories.

Contribution

It provides a general theoretical framework for understanding dissipative freezing, supported by mathematical perspectives and example systems, highlighting the role of Liouvillian spectral properties.

Findings

Dissipative freezing is a widespread consequence of strong symmetry in open quantum systems.

The spectral properties of the Liouvillian determine the occurrence and timescale of freezing.

Presence of purely imaginary eigenvalues prevents freezing, indicating preserved coherences.

Abstract

Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector to freeze into in the long-time limit. This phenomenon has been termed dissipative freezing, and in this paper we argue, by presenting several simple mathematical perspectives on the problem, that it is a general consequence of the presence of a strong symmetry in an open system with only a few exceptions. Using a number of example systems we illustrate these arguments, uncovering an explicit relationship between the spectral properties of the Liouvillian in off-diagonal symmetry sectors and the time it takes for freezing to occur. In the limiting case that eigenmodes with purely imaginary eigenvalues are manifest in these sectors, freezing fails to occur. Such modes indicate the preservation of information and coherences between symmetry sectors of the system and can lead to phenomena such as non-stationarity and synchronisation. The absence of freezing at the level of a single quantum trajectory provides a simple, computationally efficient way of identifying these traceless modes.