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

Dynamics of a qubit-oscillator system with periodically varying coupling