In this paper the interaction between a two-level atom and a single-mode field in the kphoton Jaynes-Cummings model (JCM) in the presence of Stark shift and Kerr medium is studied. All terms in the respected Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f -deformed. In particular, the effect of the initial state of radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states. To achieve this purpose, coherent, squeezed and thermal states as initial field states are considered.

The interaction between two Ξ-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.

The interaction between a ♦-type four-level atom and a single-mode field in the presence of Kerr medium with intensity-dependent coupling involving multi-photon processes has been studied. Using the generalized (nonlinear) Jaynes-Cummings model, the exact analytical solution of the wave function for the considered system under particular condition, has been obtained when the atom is initially excited to the topmost level and the field is in a coherent state. Some physical properties of the atom-field entangled state such as linear entropy showing the entanglement degree, Mandel parameter, mean photon number and normal squeezing of the resultant state have been calculated. The effects of Kerr medium, detuning and the intensity-dependent coupling on the temporal behavior of the latter mentioned nonclassical properties have been investigated. It is shown that by appropriately choosing the evolved parameters in the interaction process, each of the above nonclassicality features, which are of special interest in quantum optics as well as quantum information processing, can be revealed.[10], entanglement [11], atomic dipole squeezing [12,13] and so on. This model has been extended in different directions such as multi-mode fields [14,15,16], multi-atoms interaction [17,18], multi-level atoms [19] and Kerr nonlinearity [20]. The interaction between two-level and different types of three-level atoms with quantized cavity field have been reviewed by Yoo and Eberly in [2]. Also, in recent years, researchers have strongly focused on the nonlinear interaction between a two-or multi-level atom with cavity field which leads to the deformed JCM. The latter nonlinear JCM, which firstly suggested in [21,22] describes the dependence of atom-field coupling on the light intensity. The revival-collapse phenomenon in the quadrature squeezing has been observed in the interaction between a two-level atom with single-mode cavity field of the multi-photon intensity-dependent JCM [23]. A nonlinear Jaynes-Cummings model which constructed from the standard JCM by deforming the single-mode field operators using f -deformed oscillator introduced by Man , ko et al [24] has been studied in [25]. The nonlinear interaction between a three-level atom in Λ-and V -configuration with a twomode field under a multi-photon process has been studied respectively in [26] and [27]. The interaction between a Λ-and V -type three-level atom with intensity-dependent coupling in a Kerr medium respectively studied in [28] and [29]. Recently, one of us has studied the entanglement dynamics of the nonlinear interaction between a Λ-type three-level atom with a two-mode cavity field in the presence of a cross-Kerr medium and its deformed counterpart [30], intensitydependent atom-field coupling and the detuning parameters [31,32]. Also, the authors have investigated a three-level atom in motion which interacts with a single-mode field in an optical cavity in an intensity-dependent coupling regime [33]. Sub-Poissonian statistics, population inversion and entropy squeezi...

Entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of detuning parameter and Stark effect. It is assumed that atom-field coupling and third-order susceptibility of the Kerr medium depend on the intensity of light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom-field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in standard coherent state). Then, in order to evaluate the degree of entanglement between subsystems, we investigate the dynamics of entanglement through the well-known criteria such as von Neumann reduced entropy, entanglement of formation and negativity. Finally, we analyze the influences of Stark shift, deformed Kerr medium, intensity-dependent coupling and also detuning parameter on the above-mentioned measures, in detail. Numerical results show that the amount of entanglement between different subsystems can be controlled by choosing the evolved parameters, appropriately. Introductory remarksThe notion of entanglement, as the nonlocality aspect of quantum correlations, is a form of quantum superposition and an outstanding trait of quantum mechanics which has no classical counterpart; the concept that is known as the heart of the Einstein-Podolsky-Rosen (EPR) paradox [1] and Bell's theorem [2]. The entanglement is an essential ingredient and a cornerstone of quantum information science such as quantum computation and communication 1