We study the influence of a strong off-resonant driving signal to the energy levels of a superconducting flux qubit both experimentally and theoretically. In the experiment, we carry out a three-tone spectroscopy. This allows us to directly observe the modification of the qubits energy levels by the dynamical Stark shift caused by the driving signal. A theoretical treatment including corrections from both, rotating and counter-rotating frame, allowed us to completely explain the observed experimental results and to reconstruct the influence of the strong driving to the dissipative dynamics as well as to the coupling constants of the qubit. As one potential application, the tunability of the minimal energy-level splitting of a superconducting qubit by a microwave induced dynamical Stark shift can help to overcome the parameter spread induced by the micro fabrication of superconducting artificial quantum circuits.
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