Dissipative phase transitions (DPTs) 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 DPTs have been suggested in the literature, the most famous of which, the Liouvillian gap, can be derived from a spectral analysis of the Liouvillian superoperator that governs the complex interplay between coherent and dissipative dynamics. Here we consider the 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 DPTs, 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 already be experimentally tested in optical systems, providing a practical method to detect criticality in quantum open systems.

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• Continuous phase transition
• Magnetic order
• Open quantum systems
• Quantum measurements
• Quantum optics