  We show two examples in which the dynamical Casimir effect can be achieved by
modulating the Kerr or higher order nonlinearities. In the first case the
cavity field is coupled to an arbitrary number of qubits or an harmonic
oscillator via the dipole interaction. In the second case, the modulation of
the nonlinearities is accompanied by the off-resonance modulation of the cavity
frequency. We present the analytic description of the phenomenon and supplement
it with numeric simulations, demonstrating that photons can be created from
vacuum and the resulting hyper-Poissonian photon statistics is very different
from the squeezed vacuum state.
