Synthetic quantum matter in superconducting circuits

Superconducting circuits have emerged as a competitive platform for realizing a practical quantum computer, satisfying the challenges of controllability, long coherence and strong interactions between individual systems that are at the heart of coherent quantum computation. In this work, we apply this well-developed toolbox to a different problem: the exploration of strongly correlated phases of photonic quantum matter. The qubits of the quantum circuit become the sites of a Bose Hubbard lattice - their anharmonicity provides the on-site photon-photon interaction, couplings between them generates inter-site tunneling, while multiplexed qubit readout provides time- and site- resolved microscopy of the Bose Hubbard system. We further develop a new method for dissipative preparation and stabilization of incompressible phases of matter, achieved through reservoir engineering. We characterize our Bose-Hubbard system through coherent lattice dynamics including quantum random walks, and then connect it to the dissipative stabilizer to realize and investigate a Mott insulator of photons. These experiments demonstrate the power of superconducting circuits for studying strongly correlated physics, and with the recently demonstrated low-loss microwave Chern insulators could point the way to topological many-body states of photons.