The influence of thermal photons on the dynamics of a quantum optomechanics system with quadratic cavity-membrane couplings

In this paper we investigate the influence of thermal photons as an inevitable source of damping on the dynamics of a quantum optomechanics system consisting of a suspended membrane in an optical cavity. The membrane is putted inside the cavity, in such a way that it plays the role of a movable mirror for each subcavity. In this respect, we investigate about the tunnelling of the photons between the two subcavities as well as the dynamics of membrane position in the mean-field approximation. In particular, the influences of thermal photons (in the presence of ”photon” and ”phonon” loss rates) on the time evolution of the above-mentioned quantities are evaluated and studied through which it is observed that the thermal photons considerably affects on the population inversion of photons number whenever the square coupling constant of cavity-membrane is weak. Inversely, the influence of thermal photons on the position of membrane is more visible for strong square coupling. Furthermore, it is demonstrated that generally the discussed properties can be appropriately adjusted by tuning the involved damping parameters.