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

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 superradiant 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 through radiation pressure just like in typical optomechanical setups. We show that, in the thermodynamical limit, the superradiant phase induces a classical driving force on the mirror without causing decoherence.