Geometric discord in a dissipative double-cavity optomechanical system

In this paper, we propose a theoretical scheme to study the dynamics of the geometric measure of quantum discord (GMQD) between two non-interacting qubits in a dissipative optomechanical system composed of two Fabry-Perot cavities. In this system, each cavity contains a single-mode quantized radiation field which, in the rotating wave approximation, interacts with both mechanical resonator and two-level atom. In addition, the effects of dissipation are taken into account by considering cavity decay, losses of cavity mirror, and spontaneous emission from the atom. We start with the master equation approach and under some circumstances, we find a non-Hermitian Hamiltonian. Adopting this procedure yields the problem with an acceptable analytical solution. This means that all enough information in the study of the considered open quantum system is exactly obtained. Thereupon, we study the quantum correlations between the atoms with the help of the GMQD. It can be seen that the GMQD between two atoms can be controlled by the optomechanical coupling coefficient, the atom-field coupling strength and the dissipation parameters. Moreover, decreasing the coefficient of optomechanical coupling as well as reducing the strength of atom-field coupling improves the GMQD between two atoms. It is also mentioned that, taking the dissipation effects into account, we see that, as the time proceeds, the GMQD approaches to a stable value. In addition, eliminating the effect of spontaneous emission leads to a diminution in the amount of GMQD. Consequently, the quantum correlations between two atoms can be enhanced by considering the effect of spontaneous emission.