Dicke-type phase transition in a multimode optomechanical system

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.

14 pages, 6 figures

References in corpus (15)

• Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Cavity Opto-Mechanics with a Bose-Einstein Condensate
• Dispersive optomechanics: a membrane inside a cavity
• Cavity Nonlinear Optics at Low Photon Numbers from Collective Atomic Motion
• High quality mechanical and optical properties of commercial silicon nitride membranes
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Emergent superfluid crystals, frustration, and topologically defected states in multimode cavity QED
• Optomechanical trapping and cooling of partially transparent mirrors
• Self-organization of a Bose-Einstein condensate in an optical cavity
• Dicke-type phase transition in a spin-orbit coupled Bose-Einstein condensate
• Quantum fidelity and quantum phase transitions in matrix product states
• The optomechanical instability in the quantum regime
• Ground-state fidelity in one-dimensional gapless model
• Qantum theory of optomechanical cooling