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Weak measurements are a subset of measurement processes in quantum mechanicswherein the system which is being measured interacts very weakly with themeasuring apparatus. Measurement values of observables undergoing a weakinteraction and their amplification, are concepts that have sharpened ourunderstanding of interaction processes in quantum mechanics. Recent experimentsshow that naturally occurring processes such as resonance fluorescence fromexcited states of an atom can exhibit weak value amplification effect. In thispaper, we theoretically analyze the process of elastic resonance fluorescencefrom a V-type three level atomic system, using the well known Weiskopff-Wigner(W-W) theory of spontaneous emission. Within this theory, we show that, a weakinteraction regime can be identified and for suitable choices of initial andfinal excited states, the mean scattering time between these states show anamplification effect during interaction with the vacuum bath modes of theelectromagnetic field. We thus show for the first time that a system bathinteraction can show weak value amplification. Using our theory we reproducethe published experimental results carried out in such a system. Moreimportantly, our theory can calculate scattering timescales in elasticresonance scattering between multiple excited states of a single atom orbetween common excited state configurations of interacting multi-atom systems.

Excited to excited state scattering using weak measurements