  The scenario of a single-mode cavity with harmonically modulated frequency is
revisited in the presence of strongly detuned qubit or cyclic qutrit. It is
found that when the qubit frequency is close to $3\nu $ there is a peak in the
photon generation rate via four-photon transitions for the modulation frequency
$4\nu $, where $\nu $ is the average cavity frequency. Effective five-photon
processes can occur for the modulation frequency $5\nu $ in the presence of a
cyclic qutrit, and the corresponding transition rates exhibit series of peaks.
Closed analytical description is derived for the unitary evolution, and numeric
simulations indicate the feasibility of multi-photon dynamical Casimir effect
under weak dissipation.
