Optical properties of an atomic ensemble coupled to a band edge of a photonic crystal waveguide

We study the optical properties of an ensemble of two-level atoms coupled to a 1D photonic crystal waveguide (PCW), which mediates long-range coherent dipole-dipole interactions between the atoms. We show that the long-range interactions can dramatically alter the linear and nonlinear optical behavior, as compared to a typical atomic ensemble. In particular, in the linear regime, we find that the transmission spectrum reveals multiple transmission dips, whose properties we show how to characterize. In the many-photon regime the system response can be highly non-linear, and under certain circumstances the ensemble can behave like a single two-level system, which is only capable of absorbing and emitting a single excitation at a time. Our results are of direct relevance to atom-PCW experiments that should soon be realizable.