Quantum theory of nondegenerate multiwave mixing

A quantum theory of nondegenerate multiwave mixing in a two-level atomic medium is formulated, with emphasis on traveling-wave interaction geometries. Two equivalent alternative methods are developed to treat, with some rigor, the spatial propagation of the interacting multimode traveling-wave field. The theory is applied to the case of a single beam propagating through the medium to obtain the spectrum of squeezing. The effects of spontaneous emission, propagation loss, atomic collisions, and pump-probe phase mismatch are comprehensively taken into account for the first time.