Dipole-dipole interaction in three-dimensional optical lattices

We compute the near-resonant dipole-dipole interaction between atoms in a three-dimensional optical lattice. After a general derivation, we concentrate specifically on the case of a J=1/2=3/2 off-resonant transition, in which case the excited electronic states can be adiabatically eliminated. We present in detail the spatial dependence of the resulting effective dipole-dipole potential, and discuss the physical origin of its anisotropy. In addition to impacting the center-of-mass motion of the atoms, the effective dipole-dipole potential can induce electronic transitions within one or both atoms. The symmetries of the matrix elements corresponding to these various mechanisms are also commented upon. 1996 The American Physical Society.