Entanglement, quantum statistics and squeezing of two $Ξ$-type three-level atoms interacting nonlinearly with a single-mode field

Abstract: The interaction between two $\Xi$-type three-level atoms and a single-mode cavity field in the intensity dependent coupling regime has been studied. Exact analytical solution of the wave function for the considered atoms-field system has been obtained by using the Laplace transform technique when the atoms are initially prepared in the excited state and the field is in a coherent state. The presented structure has the potential ability to generate various new classes of entangled states depending on the chosen nonlinearity function. Two forms of intensity-dependent coupling as well as constant coupling are considered. Some important physical properties such as quantum entanglement, quantum statistics and quadrature squeezing of the corresponding states are investigated, numerically, by which the nonclassicality features of the produced entangled state are well-established. In particular, the effect of intensity-dependent coupling on the degree of entanglement between different bipartite partitions of the system (that is, "atom$+$atom"-field and "field$+$atom"-atom) using the linear entropy is investigated. At the same time, by paying attention to the negativity as a useful measure, the entanglement between the two atoms is studied in detail.