Non-degenerate forward four-wave mixing in hot atomic vapors has been shownto produce strong quantum correlations between twin beams of light [McCormicket al, Opt. Lett. 32, 178 (2007)], in a configuration which minimizes losses byabsorption. In this paper, we look at the role of the phase-matching conditionin the trade-off that occurs between the efficiency of the nonlinear processand the absorption of the twin beams. To this effect, we develop asemi-classical model by deriving the atomic susceptibilities in the relevantdouble-lambda configuration and by solving the classical propagation of thetwin-beam fields for parameters close to those found in typical experiments.These theoretical results are confirmed by a simple experimental study of thenonlinear gain experienced by the twin beams as a function of the phasemismatch. The model shows that the amount of phase mismatch is key to therealization of the physical conditions in which the absorption of the twinbeams is minimized while the cross-coupling between the twin beams ismaintained at the level required for the generation of strong quantumcorrelations. The optimum is reached when the four-wave mixing process is notfully phase matched.
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