Many-body states of radiation in a Fabry-Perot cavity coupled to a single qubit

We explore a new regime of quantum electrodynamics achieved when a strongly anharmonic qubit is coupled to a Fabry-Perot resonator with a strength greater than the free spectral range. The qubit mediates a coherent hybridization of single-photon excitations with a class of many-body states of radiation, involving several photons in the low frequency modes. We experimentally realize this new regime by galvanically coupling a fluxonium qubit to a long section of 1-D transmission line resonator and performing linear microwave spectroscopy. As a result, the nearly equidistant Fabry-Perot spectrum acquires a rich fine structure. This effect was missed in the previous theoretical studies of the superstrong coupling regime, and it is strongly suppressed for a weakly anharmonic qubit, such as transmon. We propose an effective description for the many-body spectrum which matches hundreds of energy levels without adjustable parameters.