Collapse of superradiant phase and Dicke phase transition at finite temperature in a hybrid optical-mechanical system

Abstract

In this paper, we theoretically investigate Dicke phase transition at finite temperature in a hybrid optical-mechanical system. The thermodynamic equilibrium states are presented by means of the functional path-integral approach. We plot the mean photon number of the two cavities and the corresponding phase diagram showing the effects of the coupling strength between the two cavities, the nonlinear photon-phonon interaction strength, the finite temperature, the detuning of the two cavities. The coupling strength between the two cavities can make the phase boundary of the normal phase (NP) to the superradiant phase (SP) shift left with the increase of the atom-field coupling strength. The region of the SP is suppressed completely and the SP disappears completely with the increase of the coupling strength between the two cavities or the nonlinear photon-phonon interaction strength, finally just the NP and the dynamically unstable state (DUS) exist. The nonlinear photon-phonon coupling strength just affects the turning curve, but not the phase boundary. The unstable non-zero photon number state and the SP are coexistent, similar to the optical bistability.

Collapse of Superradiant Phase and Unstable Macroscopic Vacuum State in An-Optomechanical-Dual-Cavity with a Bose-Einstein Condensate

“…At present, cavity optomechanics [1][2][3][4], which mainly study the interaction between the light field and the mechanical oscillator at low energy scale [5,6], has become an interdisciplinary field of crossing condensed matter physics, material science, optics, quantum optics and other fields. The development of cavity optomechanics provides a broad prospect for exploring the mechanical quantum properties of macroscopic objects [1,7].…”

“…With the development of double-cavity optomechanical system [48][49][50], in the past several years, a novel hybrid cavity optomechanical system consisting of a mechanical resonator and two coupled single-mode cavities has been introduced [4,8,51]. Moreover, a Bose-Einstein Condensate is trapped to the feedback cavity 2 and the mechanical oscillator couples to Cavity 1.…”

“…This opens up the possibility for applying cavity quantum optomechanics beyond the resolved sideband regime. An imaginary-time functional path integral approach has be used to study the finitetemperature properties in such system [4]. Such high-finesse system induces the SP collapses and turns to an unstable non-zero photon number beyond the turning curve, which is similar to the optical bistability.…”

“…Motivated by these works above, in this paper, we firstly present the energy functional of a Bose-Einstein Condensate in an optomechanical-dual-cavity [4,8,51] by means of the spin-coherent-state variational method [52], which is not only suitable for arbitrary number of atoms but also can take into account the inversely atomic populated state, which is necessary for the stimulated radiation and multiple stable states. The atomic population number and the mean photon number are plotted as a function of the atom-field coupling strength for the given dual-cavity coupling interaction J or the photon-phonon interaction ζ.…”

Collapse of superradiant phase and unstable macroscopic vacuum state in an-optomechanical-dual-cavity with a Bose-Einstein Condensate

“…With the development of double-cavity optomechanical system [48][49][50], in the past several years, a novel hybrid cavity optomechanical system consisting of a mechanical resonator and two coupled single-mode cavities has been introduced [4,8,51]. Moreover, a Bose-Einstein Condensate is trapped to the feedback cavity 2 and the mechanical oscillator couples to Cavity 1.…”