Driven-dissipative dynamics in superconducting circuit lattices coupled to quantum baths

Superconducting circuits have emerged as a powerful platform for quantum computing and simulation. The long coherence, strong interactions, and high tunability e.g. of coupling to the environment, make circuits ideal for exploring novel quantum many-body phases in open quantum systems. Recently, engineered dissipation is used to prepare a Mott insulator of photons in circuits by coupling a narrowband incoherent bath with a Bose-Hubbard lattice. Here, we propose experiments to explore strongly correlated lattice phases in the presence of broadband quantum baths. We discuss schemes for realizing dissipative baths with dynamically tunable spectra, and show how they can be used to create and manipulate strongly entangled lattice phases. The non-equilibrium dynamics of quantum correlations can be probed directly using site-resolved readout. The engineered baths also allow us to explore the effect of non-classical noise on interacting quantum systems. We will present results from numerical simulations and our experimental progress.