Mediating dipole-dipole-interactions using three-dimensional atomic arrays

Nanophotonic structures are widely employed to engineer the bandstructure of light and thus provide a way to tune the interactions between quantum emitters in their vicinity. To date, mostly solid-state nanophotonic structures have been explored.
Here, we propose using a simple cubic three-dimensional array of atoms to produce an omnidirectional bandgap for light and show that it enables coherent, dissipation-free interactions between embedded impurities. We show explicitly that the band gaps persist for moderate lattice sizes and finite filling fraction, which makes this effect readily observable in experiment.
Our work paves the way toward analogue spin quantum simulators with long-range interactions using ultracold atomic lattices, and is an instance of the emerging field of atomic quantum metamaterials.