Fig. 6. Controlled collisions for quantum logic can be
performed in a three dimensional optical lattice. Along
the quantization z-axis, polarization gradients trap
two different groupings of atoms, labels by their internal
states. By rotating the polarization vectors, atoms can
be brought together pair-wise for coherent interaction.
In our protocol an additional laser field acts to
excite entangling electric dipole-dipole interactions.

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