Interplay between optomechanics and the dynamical Casimir effect

We develop a model of a quantum field confined within a cavity with a movable wall where the position of the wall is quantized. We obtain a full description of the dynamics of both the quantum field and the confining wall depending on the initial state of the whole system. Both the reaction and back-reaction of the field on the wall, and the wall on the field, can be taken into account, as well as external driving forces on both the cavity and the wall. The model exactly reproduces the resonant cavity mode stimulation due to the periodic motion of the mirror (dynamical Casimir effect), as well as the standard radiation pressure effects on the quantized wall(optomechanics). The model also accounts for the interplay of the two scenarios. Finally, the time evolution of the radiation force shows the interplay between the static and dynamical Casimir effect.