Synthetic quantum materials in superconducting circuits

Superconducting circuits have emerged as a competitive platform for quantum computation, satisfying the challenges of controllability, long coherence and strong interactions. Here we apply this toolbox to the exploration of strongly correlated quantum matter, building a Bose-Hubbard lattice for photons in the strongly interacting regime. We develop a versatile recipe for the dissipative preparation of incompressible many-body phases through reservoir engineering and apply it in our system to realize the first Mott insulator of photons. Site- and time-resolved readout of the lattice allows microscopic observation of the lattice dynamics. The low entropy Mott state can serve as a starting point for studying other strongly correlated phases, e.g. a Tonks-Girardeau gas of interacting defects. The dissipative preparation demonstrated in this work also enable future exploration of elusive interacting topological phases.