Entanglement of a damped non-degenerate $\Diamond$ -type atom interacting nonlinearly with a single-mode cavity

Abstract

In this paper, we investigate the entanglement of a non-degenerate $ \Diamond$ -type four-level atom interacting with a single-mode cavity field with multi-photon transitions in the intensity-dependent (atom-field) coupling regime. We consider the non-degenerate atom in the intermediate levels and with different detunings between the frequencies of the atom and quantized light field. The decay of the atom from the topmost state to the two intermediate states and also that from the two intermediate states to the bottom state are taken into account. In spite of the fact that the system seems to be complicated, the explicit form of the state vector of the entire system is analytically obtained by using the Laplace transform technique. Then, the entanglement between the atom and field is evaluated with the help of I concurrence measure. The effects of intensity-dependent coupling, decay rates, multi-photon processes and detuning parameters on the concurrence are numerically analyzed, in detail. The results indicate that, the larger the decay coefficients, the more rapid the entanglement decrement between the atom and the field. The intensity-dependent coupling enhances the entanglement between atom and field in most of the interaction times. Furthermore, the degeneracy of the intermediate atomic levels in the presence of decay parameters increases the asymptotic value of the concurrence in the linear and nonlinear regimes. Finally, the amount of entanglement between atom and field in the presence of decay parameters for two-photon transition is greater than that for the one-photon transition.