Collective Electronic Excitation Coupling between Planar Optical Lattices using Ewald's Method

Using Ewald's summation method we investigate collective electronic excitations (excitons) of ultracold atoms in parallel planar optical lattices including long range interactions. The exciton dispersion relation can then be suitably rewritten and efficiently calculated for long range resonance dipole-dipole interactions. Such in-plane excitons resonantly couple for two identical optical lattices, with an energy transfer strength decreasing exponentially with the distance between the lattices. This allows a restriction of the transfer to neighboring planes and gives rise to excitons delocalized between the lattices. In general equivalent results will hold for any planar system containing lattice layers of optically active and dipolar materials.