  The dynamics of qubits coupled to a harmonic oscillator with time-periodic
coupling is investigated in the framework of Floquet theory. This system can be
used to model nonadiabatic phenomena that require a periodic modulation of the
qubit/oscillator coupling. The case of a single qubit coupled to a resonator
populated with $n= 0,1$ photons is explicitly treated. The time-dependent
Schr\"{o}dinger equation describing the system's dynamics is solved within the
Floquet formalism and a perturbative approach in the time- and Laplace-domain.
Good quantitative agreement is found between the analytical and numerical
calculations within the Floquet approach, making it the most promising
candidate for the study of time-periodic problems. Nonetheless, the time- or
Laplace-domain perturbative approaches can be used in the presence of aperiodic
time-dependent terms in the Hamiltonian.
