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

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.

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Cited by in corpus (8)

• Universal non-equilibrium properties of dissipative Rydberg gases
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Two-time Correlations Probing the Dynamics of Dissipative Many-Body Quantum Systems: Aging and Fast Relaxation
• Metastability in an open quantum Ising model
• Sanov and Central Limit Theorems for output statistics of quantum Markov chains
• Heisenberg versus standard scaling in quantum metrology with Markov generated states and monitored environment
• Real-time dynamics of open quantum spin systems driven by dissipative processes
• Dynamical symmetries and crossovers in a three-spin system with collective dissipation