Realizing systems that support robust, controlled interactions between individual photons is an exciting frontier of nonlinear optics. To this end, one approach that has emerged recently is to leverage atomic interactions to create strong and spatially nonlocal interactions between photons. In particular, effective photonic interactions have been successfully created via interactions between atoms excited to Rydberg levels. Here, we investigate an alternative approach, in which atomic interactions arise via their common coupling to photonic crystal waveguides. This technique takes advantage of the ability to separately tailor the strength and range of interactions via the dispersion engineering of the structure itself, which can lead to qualitatively new types of phenomena. For example, much of the work on photon-photon interactions relies on the linear optical effect of electromagnetically induced transparency, in combination with the use of interactions to shift optical pulses into or out of the associated transparency window. Here, we identify a large new class of “correlated transparency windows,” in which photonic states of a certain number and shape selectively propagate through the system. Through this technique, we show that molecular bound states of photon pairs can be created.
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