  We study a means of creating multiparticle entanglement of neutral atoms
using pairwise controlled dipole-dipole interactions in a three dimensional
optical lattice. 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 well localized center
of mass states. Different protocols are presented for implementing two-qubits
quantum logic gates such as the controlled-phase and swap gate. We analyze the
fidelity of our gate designs, imperfect 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.
