Spectral theory of non-Markovian dissipative phase transitions

TL;DR

This paper extends the spectral theory of dissipative phase transitions to non-Markovian quantum systems, broadening the understanding of phase behavior beyond memoryless environments and enabling new non-Markovian engineering possibilities.

Contribution

It generalizes the spectral theory framework to non-Markovian dynamics and demonstrates its effectiveness on a complex two-mode Dicke model where previous methods failed.

Findings

Successfully captures signatures of superradiant phase transition in a challenging model

Establishes connections between the spectrum of the non-Markovian generator and phase transitions

Broadens the applicability of dissipative phase transition analysis to non-Markovian systems

Abstract

Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the spectral theory of dissipative phase transitions to non-Markovian systems, encompassing a much broader class of quantum materials and experiments and opening many possibilities for non-Markovian engineering of matter phases such as, as explored in the companion Letter [Debecker et. al., Phys. Rev. Lett. 133, 140403 (2024)], reshaping of phase boundaries and triggering of phase transitions. We first prove several statements about the connections between the spectrum of the generator of the non-Markovian dynamics of general systems and dissipative phase transitions. Then, as a benchmark, we show that our framework can capture all the expected signatures of the superradiant phase transition appearing in a challenging $U(1)$-symmetric two-mode Dicke model from a reduced description of the dynamics of the atoms only, a task for which all other methods have failed so far.