Abstract
We study a means of creating multiparticle entanglement of neutral atoms using pairwise controlled dipole-dipole interactions. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate and substantial coherent evolution of the two-atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states; allowing for deterministic generation of entanglement. We derive selection rules and a figure of merit for the dipole-dipole interaction matrix elements; for alkali atoms with hyperfine structure and trapped in localized center of mass states. Different protocols are presented for implementing two-qubit quantum logic gates such as the controlled-phase and swap gates. We analyze the error probability of our gate designs; finite due to decoherence from cooperative spontaneous emission and coherent couplings outside the logical basis. Outlines for extending our model to include the full molecular interactions potentials are discussed.
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