Spectral Theory of Non-Markovian Dissipative Phase Transitions

Abstract

To date, dissipative phase transitions (DPTs) have mostly been studied for quantum systems coupled to idealized Markovian (memoryless) environments, where the closing of the Liouvillian gap constitutes a hallmark. Here, we extend the spectral theory of DPTs to arbitrary non-Markovian systems and present a general and systematic method to extract their signatures, which is fundamental for the understanding of realistic materials and experiments such as in the solid-state, cold atoms, cavity or circuit QED. We first illustrate our theory to show how memory effects can be used as a resource to control phase boundaries in a model exhibiting a first-order DPT, and then demonstrate the power of the method by capturing all features of a challenging second-order DPT in a two-mode Dicke model for which previous attempts had fail up to now