Symmetries and Conservation Laws in Quantum Trajectories: Dissipative Freezing

TL;DR

This paper reveals that in driven-dissipative quantum systems with strong symmetries, individual trajectories randomly select a symmetry sector, breaking conservation laws at the trajectory level, a purely quantum phenomenon with no classical counterpart.

Contribution

It demonstrates how quantum superpositions in systems with strong symmetries lead to sector selection in trajectories, challenging classical notions of conservation and phase coexistence.

Findings

Trajectories randomly collapse into single symmetry sectors.

Conservation laws break down at the individual trajectory level.

Behavior can oppose typical dissipative phase transition signatures.

Abstract

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.