Quantum-mechanical counterpart of nonlinear optics

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Abstract
Raman-type laser excitation of a trapped atom allows one to realize the quantum-mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multimode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent 'displacement' of the motional quantum state may induce strong amplitude squeezing and quantum interferences.
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