Theorem on coherent transients

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Abstract
A fundamental theorem in nuclear magnetic resonance and quantum optics is derived for an atomic system subject to inhomogeneous broadening and coherent preparation by a pulsed electromagnetic field of arbitrary shape. We show that the coherent emission, free induction decay or echo, which follows is confined to an interval which precisely equals the duration of the applied pulse sequence. The theorem applies to two-level or multilevel transitions for which the inhomogeneous linewidth is infinitely broad and the sample is optically thin.

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