Atom-atom interactions around the band edge of a photonic crystal waveguide.

Tailoring the interactions between quantum emitters and single photons constitutes one of the cornerstones of quantum optics. Coupling a quantum emitter to the band edge of a photonic crystal waveguide (PCW) provides a unique platform for tuning these interactions. In particular, the cross-over from propagating fields [Formula: see text] outside the bandgap to localized fields [Formula: see text] within the bandgap should be accompanied by a transition from largely dissipative atom-atom interactions to a regime where dispersive atom-atom interactions are dominant. Here, we experimentally observe this transition by shifting the band edge frequency of the PCW relative to the [Formula: see text] line of atomic cesium for [Formula: see text] atoms trapped along the PCW. Our results are the initial demonstration of this paradigm for coherent atom-atom interactions with low dissipation into the guided mode.