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 E(x) proportional to e(+/- ikxx) outside the bandgap to localized fields E(x) proportional to e(-kx vertical bar x vertical bar) 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 D-1 line of atomic cesium for (N) over bar = 3.0 +/- 0.5 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.