We present a fully quantum-mechanical theory of nondegenerate four-wave mixing processes in three-level cascades with a two-photon pump. The results are applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong pump intensities and tunings within the Rabi sidebands. We find good broadband squeezing for low pump intensities and tunings outside a small region around central tuning. Both cases avoid regions of significant spontaneous emission.
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