Dissipative quantum phase transitions monitored by current fluctuations

TL;DR

This paper proposes using output current fluctuations as a practical method to detect dissipative quantum phase transitions in open quantum systems, validated through models and suitable for experimental testing.

Contribution

It introduces a novel approach to identify DPTs via current fluctuation analysis, complementing spectral methods like the Liouvillian gap.

Findings

Current fluctuations show dramatic changes at the critical point.

Validation with dissipative XYZ and Kerr models confirms effectiveness.

Method is experimentally feasible in optical systems.

Abstract

Dissipative phase transitions (DPT) are defined by sudden changes in the physical properties of nonequilibrium open quantum systems and they present characteristics that have no analog in closed and thermal systems. Several methods to detect and characterize DPT have been suggested in the literature, the most famous of which -- the $\textit{Liouvillian gap}$ -- can be derived from a spectral analysis of the Liouvillian super-operator that governs the complex interplay between coherent and dissipative dynamics. Here, we consider the $\textit{output current}$, defined as the average total quantum jumps per unit time between the open quantum system and the environment. We propose that output current fluctuations, and in particular their dynamical correlations, their power spectrum, and their characteristic timescale can provide valuable information about DPT, confirming a dramatic change of behavior at the critical point. We validate our proposal using the dissipative XYZ model and the nonlinear driven-dissipative Kerr model, showing good agreement with previous estimates of the location of the critical point. Compared to previous approaches, our proposal could be already experimentally tested in optical systems, providing a practical method to detect criticality in quantum open systems.