Dynamical effects of the dipole-dipole interaction in three-dimensional optical lattices

We present a many-body theory of the dipole-dipole interaction in three-dimensional optical lattices generated by a four-beam configuration, specializing to the case of [Formula Presented] transitions. We construct a many-body interaction Hamiltonian in coordinate representation for an antiferromagnetic fcc optical lattice, the Schrödinger field operators being expanded on a basis of Wannier functions. We discuss the main characteristics of the dipole-dipole matrix elements giving rise to bound-bound and bound-free atom interactions in the lattice. Because of the anisotropy of the dipole-dipole interaction, specific directions can be favored for transport and scattering processes. Furthermore, since the dipole-dipole interaction depends on atomic magnetic quantum numbers, the dipole-dipole potential resembles a spin-dependent potential, and can give rise to atomic hopping with simultaneous change in the magnetic quantum number.