Towards stabilizing many-body interacting flat-states in circuit QED

In circuit quantum electrodynamics, systems with many types of energy spectra can be engineered, by coupling superconducting qubits and resonators. Arranging the components in certain geometries can lead to the presence of degenerate eigenstates, which -- in a large chain -- forms a dispersionless (or “flat”) band. In a flat band with nonlinearity (provided by transmon qubits), an external drive can populate strongly correlated quantum states. In this talk, we discuss experimental and theoretical progress towards realizing a circuit QED Lieb chain, a system with a gapped flat band that can be driven into a density wave state. We also discuss driven-dissipative schemes that may allow us to stabilize strongly correlated quantum states, in particular one that makes use of a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement).