Recently, theoretical studies have advertised electromagnetic resonator arrays in circuit QED, coherently coupled to artificial atoms (e.g., superconducting qubits) as a new venue for constructing quantum simulators for strongly correlated states of matter . In this Talk, we introduce the Jaynes-Cummings lattice model and discuss the Mott-Superfluid transition of light in these systems [1,2]. We also discuss a correspondence with the celebrated Bose-Hubbard model . Then, we explore the possibilities of breaking timereversal symmetry in such interacting photon systems using on-chip circulators  allowing to engineer artificial gauge fields and realize novel topological phases. Similar phases have been predicted by Raghu and Haldane in photonic crystals  and have been recently observed . Finally, we discuss the effect of interactions on topological electron band insulators .
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