  The interaction between a $\diamondsuit$-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.
