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We experimentally investigate a strongly driven GaAs double quantum dotcharge qubit weakly coupled to a superconducting microwave resonator. TheFloquet states emerging from strong driving are probed by tracing the qubit -resonator resonance condition. This way we probe the resonance of a qubit thatis driven in an adiabatic, a non-adiabatic, or an intermediate rate showingdistinct quantum features of multi-photon processes andLandau-Zener-St\"uckelberg interference pattern. Our resonant detection schemeenables the investigation of novel features when the drive frequency iscomparable to the resonator frequency. Models based on adiabatic approximation,rotating wave approximation, and Floquet theory explain our experimentalobservations.

Floquet spectroscopy of a strongly driven quantum dot charge qubit with a microwave resonator