Generalized time-coarse graining as a systematic perturbation theory beyond RWA II: Application to drive-induced qubit transitions in transmons and fluxoniums

In order to achieve rapid dispersive readout for artificial atoms in circuit QED, a strong drive can be applied to a readout resonator coupled to the atoms. However, for both transmons and fluxoniums, dispersive coupling to a strongly driven resonator may not only significantly increase the qubit relaxation rate, but also induce spurious excitations outside the computational space, even if the drive frequency is far off-resonance from any atom transition frequencies. In this talk, we present effective time-coarse grained models for transmons and fluxoniums, and derive analytical formulas for the drive-induced transition rates as well as the Purcell decay rate. We also study backreaction from the atom to the resonator, and demonstrate that it is responsible for induced resonator nonlinearity and deviations from coherent steady states.