Abstract
We present a vector quantum field theoretic description for nonlinear atom optics of a coherent ultracold atomic beam in a standing wave laser field. In the Bragg resonance regime, the standing wave laser acts as a nonlinear atomic beam splitter. The atomic nonlinearity is due to the dipole-dipole interaction between ultracold atoms which leads to self-phase and cross-phase modulation and two-wave mixing of the scattered atomic waves in the Bragg resonance regime.
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