Photon generation via the dynamical Casimir effect in an optomechanical cavity as a closed quantum system

We present an analytical and numerical analysis of the particle creation in an optomechanical cavity in parametric resonance. We treat both the electromagnetic field and the mirror as quantum degrees of freedom and study the dynamical evolution as a closed quantum system. We consider different initial states and investigate the spontaneous emission of photons from phonons in the mirror. We find that, for initial phononic number states, the evolution of the photon number can be described as a nonharmonic quantum oscillator, providing a useful tool so as to estimate the maximum and mean number of photons produced for arbitrary high energies. The efficiency of this mechanism is further analyzed for a detuned cavity as well as the possibility of stimulating the photon production by adding some initial ones to the cavity. We also find relationships for the maximum and mean entanglement between the mirror and the wall in these states. Additionally, we study coherent states for the motion of the mirror to connect this model with previous results from quantum field theory with a classical mirror. Finally, we study thermal states of phonons in the wall and the equilibration process that leads to a stationary distribution.