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Microwave driving is a ubiquitous technique for superconducting qubits(SCQs), but the dressed states description based on the conventionally usedperturbation theory cannot fully capture the dynamics in the strong drivinglimit. Comprehensive studies beyond these approximations applicable totransmon-based circuit quantum electrodynamics (QED) systems are unfortunatelyrare as the relevant works have been mainly limited to single-mode or two-statesystems. In this work, we investigate a microwave-dressed transmon coupled to asingle quantized mode over a wide range of driving parameters. We reveal thatthe interaction between the transmon and resonator as well as the properties ofeach mode is significantly renormalized in the strong driving limit. Unlikeprevious theoretical works, we establish a non-recursive, and non-Floquettheory beyond the perturbative regimes, which excellently quantifies theexperiments. This work expands our fundamental understanding of dressed cavityQED-like systems beyond the conventional approximations. Our work will alsocontribute to fast quantum gate implementation, qubit parameter engineering,and fundamental studies on driven nonlinear systems.

Resolving non-perturbative renormalization of a microwave-dressed weakly anharmonic superconducting qubit