Intermittency and dynamical Lee-Yang zeros of open quantum systems

TL;DR

This paper investigates the dynamical phase transitions in open quantum systems by analyzing high-order cumulants and Lee-Yang zeros, revealing intermittency and phase coexistence in models like the driven three-level system and dissipative Ising model.

Contribution

It introduces a method to identify dynamical phase transitions through cumulant analysis and Lee-Yang zeros, providing new insights into intermittency and phase diagrams in open quantum systems.

Findings

Identification of critical counting field values linked to intermittency

Construction of a trajectory phase diagram for the dissipative Ising model

Estimation of the transition point from ferromagnetic to paramagnetic states

Abstract

We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large deviation form with singularities of the associated cumulant generating functions - or dynamical free energies - signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase co-existence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to being paramagnetic (active).