Position and Momentum Entanglement of Dipole-Dipole Interacting Atoms in Optical Lattices: The Einstein-Podolsky-Rosen Paradox on a Lattice

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.