Superconducting qubit in a nonstationary transmission line cavity: parametric excitation, periodic pumping, and energy dissipation

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 counter-rotating wave processes responsible for the dynamical Lamb effect. We show that the periodical modulation of the resonator frequency can increase dramatically the excitation probability. Remarkably, counter-rotating wave processes, which are generally believed to be negligible, 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.