Ultrastrong light-matter interaction in a photonic crystal waveguide*

Superconducting circuits have emerged as a rich platform for emulating synthetic quantum materials composed of artificial atoms and photonic lattices. Here, we apply this toolbox for exploring the physics of a quantum impurity coupled to the many modes of a photonic crystal. In previous experiments, strongly coupling a transmon qubit to the band structure of a stepped impedance waveguide has led to the first observation of atom-photon dressed bound states. In this work, we push the coupling strength even further to go beyond the single-photon limit. Our platform consists of a fluxonium qubit galvanically coupled to a linear chain of coupled microwave resonators. Probing transport through the waveguide reveals that the propagation of a single photon becomes a many-body problem as multi-photon bound states participate in the scattering dynamics. Furthermore, we study the effective photon-photon interactions induced by the impurity by probing the inelastic scattering spectrum. The measured correlations in the emitted quadrature fields at each waveguide mode reveal signatures of multi-mode entanglement.