Quantum-Nondemolition Probing of Multiphoton Transitions between Dressed States in a Strongly Driven Jaynes--Cummings System

The response of the Jaynes--Cummings (JC) model to strong driving has been examined previously, but the origin of intriguing features near emitter--cavity resonance remains poorly understood because of the large background in conventional transmission spectroscopy. Here we introduce a spectroscopic approach for circuit quantum electrodynamics that combines strong cavity driving with quantum-nondemolition qubit readout. Separating the drive and readout substantially enhances the measurement sensitivity as compared with conventional cavity-transmission spectroscopy. With this technique, we identify the near-resonant features as multiphoton transitions between emitter--photon dressed states of the same parity, and resolve transitions between dressed states of opposite parity. Away from resonance, we also observe selective enhancement and suppression of multiphoton transitions, together with transitions involving the second excited state of the anharmonic qubit. Our approach opens a route to resolving the rich transition structure of the JC ladder and probing strongly driven light--matter interactions.