Breaking time-reversal symmetry in interacting photon lattices using a superconducting on-chip circulator

Recently, theoretical studies have advertised EM resonator arrays, coherently coupled to artificial atoms (e.g., superconducting qubits) as a new venue for constructing quantum simulators for strongly correlated states of matter [1]. Here, we explore the possibilities of breaking time-reversal symmetry in such interacting photon systems by coupling transmission line resonators via a superconducting circuit. We demonstrate that, given an external magnetic field and a mechanism for breaking particle-hole symmetry, such a circuit can produce complex phases in the hopping amplitudes for photons. Finally, we address the prospects of this scheme for studying new quantum phase transitions in interacting photon systems, and the realization of novel 2D lattices for photons, such as the Kagome lattice. \\[4pt] [1] M. J. Hartmann, F. G. S. L. Brand{\~a}o, and M. B. Plenio, Laser \& Photonics Review 2, 527 (2008), and references therein.