Fock State Generation From the Nonlinear Kerr Medium

We discuss a system comprising a nonlinear Kerr medium in a cavity driven by an external coherent field directly or through the parametric process. We assume that the system is initially in the vacuum state, and we show that under appropriate conditions, i.e., properly chosen detuning and intensity of the driving field, the one or two-photon Fock states of the electromagnetic field can be achieved.