Nonlinear interaction of a three-level atom with a two-mode field in an optomechanical cavity: Field and mechanical mode dissipations

In this paper we investigate the dynamics of f-deformed interaction (nonlinear atom-field coupling) of a three-level atom in V-configuration with a two-mode quantized field in the presence and absence of Kerr medium as well as the phonon and photon dissipations in an optomechanical cavity. We solve the associated time-dependent Schrödinger equation and arrive at the corresponding state vector at arbitrary time. In the continuation, we evaluate several nonclassical properties including atomic von Neumann entropy, atomic information entropy squeezing, sub-Poissonian statistics and atomic squeezing, numerically. Our numerical results show that, with the parameters at our disposal, we can adjust the above-mentioned properties according to our purposes. For instance, significant amount of von Neumann entropy may be achieved, in the linear and nonlinear atom-field coupling, without or even with considered dissipations. However, atomic information entropy squeezing can be observed only in the presence of nonlinear atom-field coupling by tuning the proper values of Lamb-Dicke parameter. Atomic squeezing can be seen in the presence or absence of linear and nonlinear atom-field coupling. Negative values of Mandel parameter, showing the sub-Poissonian statistics as the nonclassicality of the field can be observed with and without nonlinear atom-field coupling, however, the presence of Lamb-Dicke nonlinearity can make this effect more visible. Unless the atomic information entropy squeezing, in all above-mentioned physical phenomena stability of the evaluated parameters can be accessible via choosing appropriate parameters containing Lamb-Dicke parameter, Kerr effects, dissipation parameters, laser pumps and photon-phonon coupling.