  We consider a superconducting qubit coupled to the nonstationary transmission
line cavity with modulated frequency taking into account energy dissipation.
Previously, it was demonstrated that in the case of a single nonadiabatical
modulation of a cavity frequency there are two channels of a two-level system
excitation which are due to the absorption of Casimir photons and due to the
counterrotating wave processes responsible for the dynamical Lamb effect. We
show that the parametric periodical modulation of the resonator frequency can
increase dramatically the excitation probability. Remarkably, counterrotating
wave processes under such a modulation start to play an important role even in
the resonant regime. Our predictions can be used to control qubit-resonator
quantum states as well as to study experimentally different channels of a
parametric qubit excitation.
