Synthetic gauge field with photons

In this article, we review the recent progress in the implementation of synthetic gauge fields for photons and the investigation of new photonic phenomena, such as nonequilibrium quantum Hall physics. In the first part, we discuss the implementation of magnetic-like Hamiltonians in coupled resonator systems and provide a pedagogical connection between the transfer matrix approach and the couple mode theory to evaluate the system Hamiltonian. In the second part, we discuss the investigation of nonequilibrium fractional quantum Hall physics in photonic systems. In particular, we show that driven strongly interacting photons exhibit interesting many-body behaviors which can be probed using the conventional optical measurement techniques.