Abstract
We employ a vector quantum field theory to describe the interaction of a coherent atomic beam with a standing-wave laser field. The coherent atomic beam is assumed to be composed of degenerate bosonic atoms. We derive a nonlinear Schr\"odinger equation to describe the diffraction of the coherent atomic beam through the standing-wave laser field in the adiabatic regime of interaction of atoms with a light wave. Under appropriate conditions, we find that the standing-wave laser field acts as a quantum nonlinear atomic beam splitter for a coherent atomic beam. The quantum correlations in the nonlinear atomic beam splitter are analyzed and the analogy to quantum correlations of nonclassical light in an optical Kerr-type medium is discussed.
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