Topological Physics with Photons

In this chapter, we review the recent progress in the implementation of synthetic gauge fields for photons and the investigation of topological features such as quantum Hall physics in photonic systems. We first 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. Furthermore, 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. Finally, we present a scheme to implement three-body interaction in circuit-QED architecture to realize some of the fractional quantum Hall parent Hamiltonians with Pfaffian wavefunction as ground state.