Quantum impurity simulation in a photonic crystal with superconducting circuits*

Superconducting circuits have emerged as a rich platform for emulating synthetic materials composed of artificial atoms and photonic lattices. Here, we apply this toolbox for exploring the physics of a quantum impurity coupled to a photonic crystal. In previous experiments, strongly coupling a transmon qubit to the band structure of a stepped impedance waveguide filter 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 photonic crystal implemented as a linear array of 26 coupled microwave resonators, and a fluxonium qubit galvanically coupled to one resonator site. Tuning the coupling strength, we can reach a regime where counterrotating terms become relevant and multiphoton bound states participate in the single-photon scattering dynamics. Additionally, by probing the transmission response for each discrete bath mode subject to a qubit drive, we can extract the spin-bath susceptibilities that capture the many-body correlations between the impurity and the harmonic degrees of freedom in the crystal.