  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.
