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We investigate a four-state system interacting with long and short laserpulses in a weak probe beam approximation. We show that when all lasers aretuned to the exact unperturbed resonances, part of the four-wave mixing (FWM)field is strongly absorbed. The part which is not absorbed has the exactintensity required to destructively interfere with the excitation pathwayinvolved in producing the FWM state. We show that with this three-photondestructive interference, the conversion efficiency can still be as high as25%. Contrary to common belief,our calculation shows that this process, wherean ideal one-photon electromagnetically induced transparency is established, isnot most suitable for high efficiency conversion. With appropriatephase-matching and propagation distance, and when the three-photon destructiveinterference does not occur, we show that the photon flux conversion efficiencyis independent of probe intensity and can be close to 100%. In addition, weshow clearly that the conversion efficiency is not determined by the maximumatomic coherence between two lower excited states, as commonly believed. It isthe combination of phase-matching and constructive interference involving thetwo terms arising in producing the mixing wave that is the key element for theoptimized FWM generation. Indeed, in this scheme no appreciable excited stateis produced, so that the atomic coherence between states |0> and |2> is alwaysvery small.Comment: Submitted to Phys. Rev. A, 7 pages, 4 figure

Consequences of induced transparency in a double-Λ scheme: Destructive interference in four-wave mixing