Synthetic gauge fields in Jaynes-Cummings-Hubbard ring lattices

Recently there has been much interest in many-body physics with photons in circuit-QED arrays. Here we explore the physics of a Jaynes-Cummings-Hubbard ring lattice subject to a synthetic gauge field, i.e.~where the hopping terms carry a complex phase factor due to Josephson couplers between the resonators. There are critical phase twists at which the single-particle spectrum is degenerate so that even weak interactions can give rise to strong correlations. We compare to ultracold bosons in rotating ring lattices and study the out-of-equilibrium physics as relevant for current experiments.