Theoretical description of two ultracold atoms in finite 3D optical   lattices using realistic interatomic interaction potentials
  A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is treated using an exact diagonalization (configuration-interaction) approach. The orthorhombic symmetry of an optical lattice with three different but orthogonal lattice vectors is explicitly considered as is the Fermionic or Bosonic symmetry in the case of indistinguishable particles. 
Sergey Grishkevich, Simon Sala and Alejandro Saenz
physics.atom-ph cond-mat.quant-gas quant-ph