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Entangling Dipole-Dipole Interactions and Quantum Logic in Optical Lattices
Gavin K. Brennen and Ivan H. Deutsch Center for Advanced Studies, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131 Poul S. Jessen Optical Sciences Center, University of Arizona, Tucson, Arizona 85721
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.