  We develop a microscopic toy model for Cavity dynamical Casimir effect (DCE),
namely, the photon generation from vacuum due to a nonstationary dielectric
slab in a fixed single mode cavity. We represent the slab by $N\gg 1$
noninteracting two-level atoms coupled to the field via the standard dipole
interaction. We show that the DCE is contained implicitly in the light-matter
interaction Hamiltonian when its parameters are externally prescribed functions
of time. We also predict several new phenomena, such as saturation of the
photon growth due to effective Kerr nonlinearity, generation of pairs of atomic
excitations instead of photons ("Inverse DCE") and coherent annihilation of
pair of system excitations due to the atomic modulation ("Anti-DCE"). These
results are extended to the circuit QED architecture, where similar effects can
be implemented with a single qubit providing an alternative way to generate
cavity and atom-field entangled states.
