Collective Dynamics of Bose--Einstein Condensates in Optical Cavities

TL;DR

This paper explores the complex collective dynamics and non-equilibrium phase transitions in Bose--Einstein condensates within optical cavities, considering cavity leakage and back-reaction effects, and predicts various oscillatory behaviors.

Contribution

It establishes a detailed phase diagram for the system, including regimes of collective dynamics and non-equilibrium transitions, incorporating key effects like cavity leakage and back-reaction.

Findings

Identification of distinct dynamical regimes separated by non-equilibrium phase transitions

Prediction of critical slowing down near phase boundaries and its enhancement by cavity losses

Description of persistent optomechanical oscillations and multi-phase coexistence regions

Abstract

Recent experiments on Bose--Einstein condensates in optical cavities have reported a quantum phase transition to a coherent state of the matter-light system -- superradiance. The time dependent nature of these experiments demands consideration of collective dynamics. Here we establish a rich phase diagram, accessible by quench experiments, with distinct regimes of dynamics separated by non-equilibrium phase transitions. We include the key effects of cavity leakage and the back-reaction of the cavity field on the condensate. Proximity to some of these phase boundaries results in critical slowing down of the decay of many-body oscillations. Notably, this slow decay can be assisted by large cavity losses. Predictions include the frequency of collective oscillations, a variety of multi-phase co-existence regions, and persistent optomechanical oscillations described by a damped driven pendulum. These findings open new directions to study collective dynamics and non-equilibrium phase transitions in matter-light systems.