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We investigate analytically and numerically the nonstationary circuit QEDsetup in which $N$ independent qubits interact with a single mode of theElectromagnetic field confined in a resonator. We consider the harmonic timemodulation of some parameter (atomic transition frequency or the atom-fieldcoupling strength) and derive the unitary dynamics up to the second order inthe modulation depth for $N=1$ and $N\gg 1$. It is shown that all the resonantphenomena that occur for modulation frequencies $\sim 2\omega _{0}$ (where$\omega _{0}$ is the cavity frequency) also occur for the halved frequencies.However, in the latter case the associated transition rates are significantlysmaller and the modulation of the coupling strength is less effective. Thetransition rates are evaluated explicitly and the prospects of employing thesecond-order resonances in the phenomena related to the dynamical Casimireffect are examined.

Analytical comparison of the first- and second-order resonances for implementation of the dynamical Casimir effect in nonstationary circuit QED