Kerr cat states from the four-photon Jaynes-Cummings model

We investigate the dynamics of a four-photon Jaynes-Cummings model for large photon number. It is shown that at certain times the cavity field is in a pure state which is a superposition of two Kerr states, analogous to the Schr\"{o}dinger cat state (superposition of two coherent states) which occurs in the one and two photon cases.