Multi-photon Transitions in an Anharmonic Quantum Oscillator: Probing the AC Stark Shifts of Higher Levels under Field Drive*

We report on the investigation of a superconducting anharmonic multi-level circuit under the influence of a detuned and strong microwave drive. We observe the AC-Stark shift of the transition frequencies caused by the applied drive and demonstrate that this shift depends on the anharmonicity, the drive amplitude and the detuning between drive and transition frequency. For large detunings we find the shift to be linear to the power of the drive, whereas for small detunings, a more complex expression for the individual transitions is calculated. Experimentally, multi-photon transitions via virtual energy levels of our system up to the third excited state are studied and shifts larger than the anharmonicity of the system are observed. The measured AC-Stark shift of higher order multi-photon transitions under increasing drive amplitude is demonstrated to be in good agreement with the analytic model and numerical simulations.