A dissipatively stabilized Mott-insulator of photons

The rich physics of strongly-correlated quantum materials can be explored in synthetic systems built with microwave photons in superconducting circuits in the circuit QED paradigm. However, the intrinsic loss in photonic platforms makes many-body quantum state preparation a challenge. 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 interaction. We employ an engineered reservoir to realize a dissipatively stabilized site and couple it to the lattice to stabilize a n=1 Mott insulator. Site-resolved microscopy allow detailed studies of the thermalization process through the dynamics of defect propagation and removal in the Mott phase. By probing two-site correlations, we could investigate the emergence of correlations and entanglement in these driven-dissipative systems.