New approach to the superconducting qubit within a microcavity

We present a novel approach for studying the dynamics of a superconducting qubit in a cavity. We succeed in linearizing the Hamiltonian through the application of an appropriate unitary transformation followed by a rotating wave approximation (RWA). For certain values of the parameters involved, we show that it is possible to obtain specific hamiltonians. As an example, we show the existence of long time-scale revivals (super-revivals) for the excitation the qubit inversion.