Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state

TL;DR

This paper introduces a dynamical approach to characterize phase transitions in open quantum systems through quantum jump trajectories, revealing phenomena beyond stationary state analysis, especially in many-body and glassy systems.

Contribution

It develops a framework to identify dynamical phase transitions using trajectory statistics, extending beyond stationary state properties, and applies it to complex quantum models including glasses.

Findings

Dynamical phase transitions can be detected via trajectory analysis.

Transitions are linked to collective phenomena in many-body systems.

Dissipative quantum glasses exhibit diverse dynamics despite identical stationary states.

Abstract

We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of the steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions. We illustrate this in open models of increasing complexity: a three-level system, a dissipative version of the quantum Ising model, and the micromaser. In these examples dynamical transitions are accompanied by clear changes in static behavior. This is however not always the case, and in general dynamical phase behavior needs to be uncovered by observables which are strictly dynamical, e.g. dynamical counting fields. We demonstrate this via the example of a class of models of dissipative quantum glasses, whose dynamics can vary widely despite having identical (and trivial) stationary states.