Autonomous Stabilizer for Gapped Photonic Many-Body States

Photonic systems are a promising platform for new physics in the regime of strongly interacting and highly correlated quantum materials. We present an eight-site strongly interacting Bose-Hubbard lattice in the Circuit QED platform along with an autonomous scheme to stabilize the coupled qubit system into a gapped manybody state. We study the N=1 Mott insulating state of our Bose lattice and characterize the performance of our thermalizer in repumping to this manybody state. This allows us to perform several experiments including quantum random walks, repumping rates of individual lattice modes, and magnetic phases.