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We propose a nanophotonic platform for topological quantum optics. Our systemis composed of a two-dimensional lattice of non-linear quantum emitters withoptical transitions embedded in a photonic crystal slab. The emitters interactthrough the guided modes of the photonic crystal, and a uniform magnetic fieldgives rise to large topological band gaps and an almost completely flattopological band. Topological edge states arise on the boundaries of the systemthat are protected by the large gap against missing lattice sites and to theinhomogeneous broadening of emitters. These results pave the way for exploringtopological many-body states in quantum optical systems.

Topological quantum optics using atom-like emitter arrays coupled to photonic crystals