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