Probing Multi-Site Correlators in a Bose Hubbard lattice*

Strongly-correlated quantum materials can be studied synthetically using the flexible toolset of microwave photons and superconducting circuits in the circuit QED paradigm. We build a 1D Bose-Hubbard lattice for photons where capacitively coupled transmon qubits serve as lattice sites, and the transmon anharmonicity corresponds to strong photon-photon collisions. In previous work, we employed an engineered reservoir to realize a dissipatively stabilized site and couple it to the lattice to prepare a n=1 Mott insulator. Recent improvements to our experiment will allow us to probe multi-site correlations. We discuss prospects for preparing and probing superfluids, and exploring the response of quantum fluctuations in the presence/absence of the stabilizer. These efforts can shed light on the intricate interplay of correlations, entanglement and thermalization in these driven-dissipative systems.