Quantum impurity ultrastrongly coupled to a photonic crystal waveguide*

Superconducting circuits have emerged as a rich platform for emulating synthetic quantum materials composed of artificial atoms and photonic lattices. In this work, we apply this toolbox for exploring the physics of a quantum impurity coupled to the many discrete modes of a photonic crystal lattice. In previous work, 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 experiment, the light-matter coupling strength is pushed into the ultrastrong coupling regime, where the qubit is simultaneously hybridized with many modes and the total number of excitations is not conserved. 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. Signatures of multi-mode entanglement are inferred from measuring correlations in the emitted quadrature fields at each waveguide mode. Our results highlight a single nonlinear impurity ultrastrongly coupled to a discrete photonic bath as a novel platform for studying many-body physics with interacting photons and generating multi-mode entanglement.