Dynamics of an atomic system associated with a cavity-optomechanical system

This paper introduces the effective Hamiltonian of two two-level atoms inside a cavity with a movable mirror. The temporal evolution of the output density state that includes the interaction between movable mirror, atoms, and field is obtained. The dynamical properties of the quantum correlations of the system are studied via l(1)-norm of coherence, Entanglement of Formation (EoF) and Bell non-locality. The results shown that the phenomena of coherence, and non-locality are approached to the degree of entanglement as the initial atomic state is set in an excited state. However, different chaotic behavior is generated for the coherence at the initially mixed state. Overall, the temporal evolution of entanglement is an intermediate correlation that lies in between coherence and normalized Bell non-locality.