The amplitude of the cavity pump field and dissipation effects on the entanglement dynamics and statistical properties of an optomechanical system

In this paper we consider a cavity optomechanics consists of a two-level atom that interacts with a single-mode quantized field in the presence of a strong driving laser. By evaluating the effective Hamiltonian of the whole system which contains the field dissipation, we derive the time-dependent state vector of the system corresponding to particular initial conditions for the cavity field and oscillatory mirror. In the continuation, we pay our attention to the dynamical properties of the considered system by choosing different initial conditions for the atom. In particular, the effects of amplitude of the pump field, various initial atomic states and cavity loss rate on the entanglement, atomic population inversion and photon and phonon statistical properties are numerically analysed. According to the obtained results, maximal entanglement for all chosen initial states of the system is visible as time develops. Moreover, the presence of dissipative field leads to decrease the entanglement and finally tends to a fixed positive value, while the Mandel parameter as well as the population inversion reduce and tend to a fixed value in the negative region. Also, the appearance of non-classicality feature such as typical collapse-revival phenomenon in the (negative values of) Mandel parameter is noticeable.