Dark Area Theorem

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We report the discovery of a "dark area theorem," a new quantum optical relation for propagation of unmatched pulses in thick three-level $Λ$-type media. We define dark area and derive the dark area theorem for a coherently prepared and inhomogeneously broadened lambda medium. We also obtain the first equation for the spatial evolution of the dark state amplitude prior to pulse-matching.
8 pages, 4 figures

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