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We show that for the two widely used configurations of the double-Λ atom-light coupling scheme, one where the control fields are applied in the same Λ-subsystem and another where they are applied in different Λ-subsystems, the forward propagation of the probe and signal fields is described by the same set of equations. We then use optimal control theory to find the spatially dependent optimal control fields that maximize the conversion efficiency from the probe to the signal field, for a given optical density. This work can find applicat
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