Probing the quantum phase transition in the Dicke model through mechanical vibrations

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This paper is concerned with quantum dynamics of a system coupled to a critical reservoir. In this context, we employ the Dicke model which is known to exhibit a super radiant quantum phase transition (QPT) and we allow one of the mirrors to move under a linear restoring force. The electromagnetic field couples to the movable mirror though radiation pressure just like in typical optomechanical setups. We show that, in the thermodynamical limit, the super-radiant phase induces a classical driving force on the mirror without causing decoherence.