Proposal for Translational Entanglement of Dipole-Dipole Interacting Atoms in Optical Lattices

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.

Figure 1

Proposed scheme of the translational EPR: two overlapping optical lattices displaced from each other in the $y$ direction by $l$ are sparsely occupied by two kinds of atoms. Each of the two kinds of atoms feels a different lattice; the shaded regions depict the energy minima (potential wells) of the lattices.

Figure 2

Joint probability distribution of the positions of two lithium atoms in adjacent optical lattices, prepared in a diatom state as specified in the text, using the ground state of the external harmonic potential with half-width of ${\sigma }_E=6a$ and temperature of 10 nK. Inset: Position probability of atom 2 in the state above, conditional on atom 1 being measured at site 0 (solid line). Dashed line: Gaussian approximation of the Wannier function with the half-width $\sigma =0.14a$.

Figure 3

Conditional probability of the momentum of atom 2 after the momentum of atom 1 has been measured for lithium diatoms prepared as in the text (the measured value $p_1=p_{1\mathrm{M}}$ is indicated with an arrow). The dashed line corresponds to the marginal probability distribution of momentum $p_2$ irrespective of the momentum of atom 1 at the temperature $T=100\mathrm{n}\mathrm{K}$. The half-width of each peak is equal to $1/s$ of Eq. (4). Inset: joint probability distribution of the atomic momenta in the state above with $T=100\mathrm{n}\mathrm{K}$.