Effects of Measurement Power on State Discrimination and Dynamics in a Circuit-Qed Experiment

We explore the effects of driving a cavity at a large photon number in acircuit-QED experiment where the “matter-like” part corresponds to an uniqueAndreev level in a superconducting weak link. The three many-body states of theweak link, corresponding to the occupation of the Andreev level by 0, 1 or 2quasiparticles, lead to different cavity frequency shifts. We show how thenon-linearity inherited by the cavity from its coupling to the weak linkaffects the state discrimination and the photon number calibration. Botheffects require treating the evolution of the driven system beyond thedispersive limit. In addition, we observe how transition rates between thecircuit states (quantum and parity jumps) are affected by the microwave power,and compare the measurements with a theory accounting for the “dressing” ofthe Andreev states by the cavity.