  We experimentally investigate a strongly driven GaAs double quantum dot
charge qubit weakly coupled to a superconducting microwave resonator. The
Floquet states emerging from strong driving are probed by tracing the qubit -
resonator resonance condition. This way we probe the resonance of a qubit that
is driven in an adiabatic, a non-adiabatic, or an intermediate rate showing
distinct quantum features of multi-photon processes and
Landau-Zener-St\"uckelberg interference pattern. Our resonant detection scheme
enables the investigation of novel features when the drive frequency is
comparable to the resonator frequency. Models based on adiabatic approximation,
rotating wave approximation, and Floquet theory explain our experimental
observations.
