Spectrum of a Resonator Coupled to a Driven Superconducting Qubit in the Strong Dispersive Regime of Circuit Quantum Electrodynamics

The resonator spectrum in the strong dispersive coupling regime of circuit-QED has been a useful nondestructive indicator of a stationary qubit state. Here we present experimental observation of the further modification of the resonator spectrum as the qubit undergoes the dynamic transition by a resonant driving field. The quartet resonance associated with the polarized qubit is observed for the resonant driving at one-photon as well as the multi-photon transition in a 3D transmon qubit. The evolution of the resonance as a function of the driving power and the detuning of the driving field is well understood by a simple model which is based on the analytic diagonalization of Hamiltonian and described in terms of dressed states, Lamb shift, and AC Stark shift.