Optomechanical effect on the Dicke quantum phase transition and quasi-particle damping in a Bose-Einstein Condensate: A new tool to measure weak force

We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom-photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity-laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.