Limit Cycle Phase and Goldstone Mode in Driven Dissipative Systems

TL;DR

This paper explores quantum phase transitions in a three-mode cavity system, revealing spontaneous symmetry breaking and Goldstone modes, with quantum fluctuations affecting coherence, and highlights potential experimental platforms for studying these phenomena.

Contribution

It introduces a theoretical framework for understanding symmetry breaking and Goldstone modes in driven dissipative quantum systems, incorporating quantum noise effects.

Findings

Spontaneous breaking of U(1) and TTS symmetries in the mean-field limit cycle phase

Emergence of a fully squeezed state linked to Goldstone mode

Quantum fluctuations limit the coherence time of the Goldstone mode

Abstract

In this article, we theoretically investigate the first- and second-order quantum dissipative phase transitions of a three-mode cavity with a Hubbard interaction. In both types, there is a mean-field limit cycle phase where the local U(1)symmetry and the time-translational symmetry (TTS) of the Liouvillian super-operator are spontaneously broken (SSB). This SSB manifests itself through the appearance of an unconditionally and fully squeezed state at the cavity output, connected to the well-known Goldstone mode. By employing the Wigner function formalism hence, properly including the quantum noise, we show that away from the thermodynamic limit and within the quantum regime, fluctuations notably limit the coherence time of the Goldstone mode due to the phase diffusion. Our theoretical predictions suggest that interacting multimode photonic systems are rich, versatile testbeds for investigating the crossovers between the mean-field picture and quantum phase transitions. A problem that can be investigated in various platforms including superconducting circuits, semiconductor microcavities, atomic Rydberg polaritons, and cuprite excitons.