Abstract
We suggest a technique to engineer entangled states in the atomic external degrees of freedom by atomic Bragg scattering from an optical lattice. We prepare two super-cooled two-level atoms in their ground state and in certain linear momentum states, and study their interaction with a cavity field which is in a superposition state. Bragg scattering of the atoms from an optical lattice generates conditional evolution in the external degrees of freedom of the atoms. By controlling the atomic interaction time with the optical field and varying initial conditions, we generate complete set of EPR-Bell basis for two incident atoms and GHZ states for more than two atoms.
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