Nonclassical Correlations in Lossy Cavity Optomechanics with Intensity-Dependent Coupling

In this paper, we describe a double-optomechanical system which contains two lossy cavities, where each cavity includes a single-mode quantized field coupled to a single vibrational mode of a flexible membrane. There exists an interaction between a two-level atom and the cavity mode in the rotating wave approximation, with degenerate multi-photon transition in the presence of intensity-dependent coupling. Furthermore, we consider the effect of different sources of dissipation consisting of cavity decay, losses of cavity mirror, and spontaneous emission from the atom. We then start with the master equation to study the dynamics of considered quantum system. Afterward, we show that under some circumstances, the solution of the complicated problem via the master equation is reduced to the determination of the state vector in the time-dependent Schrödinger equation, with the help of an effective non-Hermitian Hamiltonian. Obtaining the explicit form of the state vector of the entire system, we study the nonclassical correlations of two atoms by means of geometric discord. We also examine the roles of intensity-dependent nonlinearity function, number of photons contributed to atomic transition, number of photons in the Fock states, and different sources of dissipation in the dynamics of geometric discord of the atoms. The numerical results indicate that the steady-state value of geometric discord can be revealed, and can appropriately be controlled via the mentioned-above effects. It can be found that the existence of spontaneous emission not only protects the nonclassical correlations of the atoms but also tends the geometric discord to a steady-state value.