Engineering the electromagnetic environment of a quantum optical emitter can give rise to a plethora of exotic light-matter interactions. As one prominent example, photonic lattices can seed long-lived atom-photon bound states, in which a photon becomes confined around the atom trying to emit it.
Here, we experimentally explore this exotic atom-field interaction and access previously unexplored regimes, using a novel microwave architecture consisting of an array of compact superconducting resonators in which we have embedded two frequency-tunable artificial atoms. Among the key results, we demonstrate coherent interactions between two atom-photon bound states, in both resonant and dispersive regimes, that are suitable for the implementation of quantum computing gates. The presented architecture holds promise for quantum simulation with tunable-range interactions and photon transport experiments in the nonlinear regime.