Following the measurement of topological invariants in silicon ring resonator systems , I discuss the progress on investigation of quantum transport of light in the presence of synthetic gauge fields, with and without strong interaction. First, in the absence of interaction, we analyze the transport properties of two-photon wavefunctions in a disordered structure with protected topological edge bands, and examine the robustness of quantum transport properties . Moreover, I discuss a design for photonic crystals with topological properties . Such structures can be integrated with nonlinear quantum emitters such as color centers to mediate strong interaction. In the second part, I discuss the strongly interacting driven-dissipative regime of photons, where surprises can be seen even in a driven-dissipative 1D Bose-Hubbard model . More specifically, I will talk about the possibility of realization of topologically ordered states, such as Laughlin states, in photonic systems in the driven-dissipative regime. Finally, the effect of interacting disorder in these systems and the stability of these states will be examined .
 Wade DeGottardi, M.H. in prep.
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