  We study the dynamical Casimir effect in an electromagnetic cavity containing
a Kerr medium. We obtain approximate expressions for the time evolution
operator as well as for the number operator in the Heisenberg representation.
We have found that the generation of photons from quantum vacuum is strongly
affected by the presence of the Kerr medium, sharing physical features with the
case of two two-level atoms in a cavity with oscillating walls. The nonlinear
medium produces a saturation effect in the photon generation which shows strong
oscillations whose frequency increases with the intensity of the nonlinear
medium. We expect that these results could be relevant for any experimental
study involving the dynamical Casimir effect that is willing to incorporate
Kerr nonlinearities.
