Observation of Higher-Order Sideband Transitions and First-Order Sideband Rabi Oscillations in a Superconducting Flux Qubit Coupled to a SQUID Plasma Mode

We report results of spectroscopic measurements and time-domain measurements of a superconducting flux qubit. The dc superconducting quantum interference device (SQUID), used for readout of the qubit, and a shunt capacitor formed an LC resonator generating a SQUID plasma mode. Higher-order red and blue sidebands were observed in a simple measurement scheme because the resonant energy of the resonator, 600 MHz, was comparable to the thermal energy. We also observed Rabi oscillations on the carrier transition and the first-order sideband transitions. Because the qubit was coupled to a single arm of the dc SQUID, the qubit-SQUID coupling was significant at zero bias current, where these phenomena were observed. The ratios between the Rabi periods for the carrier transition and the sideband transitions are compared with those estimated from the coupling constant, which was separately determined. The result may be explained by assuming initial excitation of the resonator.