The model for describing the atom cavity field interaction including Kerr effect and Stark effect is studied. The two effects only influence the detuning which depends on a conservative operator of the system. Under certain conditions, the two effects have the same influences on the atom field interaction. The antibunching effect of the field is discussed when the initial field is in a macroscopic quantum superposition states. We also investigated how to obtain the solution of atom field interaction in a generalized Kerr medium.