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A cavity quantum electrodynamical (QED) system beyond the strong-couplingregime is expected to exhibit intriguing quantum phenomena. Here we report adirect measurement of the photon-dressed qubit transition frequencies up tofour photons by harnessing the same type of state transitions in anultrastrongly coupled circuit-QED system realized by inductively coupling asuperconducting flux qubit to a coplanar-waveguide resonator. This demonstratesa convincing observation of the photon-dressed Bloch-Siegert shift in theultrastrongly coupled quantum system. Moreover, our results show that thephoton-dressed Bloch-Siegert shift becomes more pronounced as the photon numberincreases, which is a characteristic of the quantum Rabi model.

Photon-Dressed Bloch-Siegert Shift in an Ultrastrongly Coupled Circuit Quantum Electrodynamical System