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Atom-mediated spontaneous parametric down-conversion in periodic waveguides.

We propose the concept of atom-mediated spontaneous parametric down-conversion, in which photon-pair generation can take place only in the presence of a single two-level emitter, relying on the bandgap evanescent modes of a nonlinear periodic waveguide. Using a guided signal mode, an evanescent idler mode, and an atom-like emitter with the idler's transition frequency embedded in the structure, we find a heralded excitation mechanism, in which the detection of a signal photon outside the structure heralds the excitation of the embedded emitter. We use a rigorous Green's function quantization method to model this heralding mechanism in a 1D periodic waveguide and determine its robustness against losses.