  We study a possible realization of the position- and momentum-correlated
atomic pairs that are confined to adjacent sites of two mutually shifted
optical lattices and are entangled via laser-induced dipole-dipole
interactions. The Einstein-Podolsky-Rosen (EPR) ``paradox'' [Phys. Rev. 47, 777
(1935)] with translational variables is then modified by lattice-diffraction
effects. This ``paradox'' can be verified to a high degree of accuracy in this
scheme.
