  We study theoretically the non-stationary circuit QED system in which the
artificial atom transition frequency has a small periodic modulation in time,
prescribed externally. We show that, in the dispersive regime, when the
modulation periodicity meets the `resonances', the dynamics may be described by
the dynamical Casimir effect, Jaynes-Cummings or Anti-Jaynes-Cummings effective
Hamiltonians. In the resonant atom-cavity regime, under the modulation
`resonance' the dynamics resembles the behavior of the dynamical Casimir effect
in a vibrating cavity containing a resonant two-level atom, and entangled
states with two photons can be created from vacuum. Thus, an analog of the
dynamical Casimir effect may be simulated in circuit QED, and several photons,
as well as entangled states, can be generated from vacuum due to the
anti-rotating term in the Rabi Hamiltonian.
