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

Microwave driving is a ubiquitous technique for superconducting qubits (SCQs), but the dressed states description based on the conventionally used perturbation theory and rotating wave approximation cannot fully capture the dynamics in the strong driving limit. Comprehensive experimental works beyond these approximations applicable for transmons is unfortunately rare, which receive rising interests in quantum technologies. In this work, we investigate a microwave-dressed transmon over a wide range of driving parameters. We find significant renormalization of Rabi frequencies, energy relaxation times, and the coupling rates with a readout resonator, all of which are not quantified without breaking the conventional approximations. We also establish a concise non-Floquet theory beyond the two-state model while dramatically minimizing the approximations, which excellently quantifies the experiments. This work expands our fundamental understanding of time-periodically driven systems and will have an important role in accurately estimating the dynamics of weakly anharmonic qubits. Furthermore, our non-Floquet approach is beneficial for theoretical analysis since one can avoid additional efforts such as the choice of proper Floquet modes, which is more complicated for multi-level systems.