**
Following the measurement of topological invariants in silicon ring
resonator systems [1], 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 [2].
Moreover, I discuss a design for photonic crystals with topological
properties [3]. 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 [4]. 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 [5].
**

**
[1]
http://lanl.arxiv.org/abs/1504.00369
[2]
http://lanl.arxiv.org/abs/1605.04894
[3]
http://lanl.arxiv.org/abs/1605.08822
[4]
http://lanl.arxiv.org/abs/1601.06857
[5] Wade DeGottardi, M.H. in prep.
**

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