Dicke-type phase transition in a multimode optomechanical system

TL;DR

This paper demonstrates a phase transition in a multimode optomechanical system resembling the Dicke model, showing symmetry breaking and critical behavior similar to second order phase transitions, with potential for experimental realization.

Contribution

It establishes a connection between optomechanical systems and Dicke-type phase transitions, analyzing critical behavior and universality class through mean-field and dynamical methods.

Findings

Identifies a symmetry-breaking bifurcation in the optomechanical system.

Shows the phase transition shares critical exponents with the Dicke model.

Discusses experimental parameters for observing the transition.

Abstract

We consider the "membrane in the middle" optomechanical model consisting of a laser pumped cavity which is divided in two by a flexible membrane that is partially transmissive to light and subject to radiation pressure. Steady state solutions at the mean-field level reveal that there is a critical strength of the light-membrane coupling above which there is a symmetry breaking bifurcation where the membrane spontaneously acquires a displacement either to the left or the right. This bifurcation bears many of the signatures of a second order phase transition and we compare and contrast it with that found in the Dicke model. In particular, by studying limiting cases and deriving dynamical critical exponents using the fidelity susceptibility method, we argue that the two models share very similar critical behaviour. For example, the obtained critical exponents indicate that they fall within the same universality class. Away from the critical regime we identify, however, some discrepancies between the two models. Our results are discussed in terms of experimentally relevant parameters and we evaluate the prospects for realizing Dicke-type physics in these systems.