Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices

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We describe a general technique that allows to induce and control strong interaction between spin states of neighboring atoms in an optical lattice. We show that the properties of spin exchange interactions, such as magnitude, sign, and anisotropy can be designed by adjusting the optical potentials. We illustrate how this technique can be used to efficiently ``engineer'' quantum spin systems with desired properties, for specific examples ranging from scalable quantum computation to probing a model with non-trivial topological orders that supports exotic non-abelian anyonic excitations.