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Paper: The Kramers-Heisenberg Coherency Matrix
Volume: 526, Solar Polarization Workshop 8
Page: 49
Authors: Stenflo, J. O.
Abstract: Scattering of light is governed by the Kramers-Heisenberg formula, which is an expression for the scattering probability amplitude. While it provides a well established foundation for scattering theory, its application to the derivation of observable quantities in the case of multi-level atomic systems is not straightforward. One has to sum over all the possible bilinear products of the scattering amplitudes for all the combinations of sublevels in the ground state and the excited state and then do ensemble averaging to construct the coherency matrix that directly relates to observable quantities like the Stokes parameters. Previous applications of density matrix theory to radiative scattering have from the outset excluded valid interference effects by doing ensemble averaging of the atomic system before the scattering processes and thereby (in the absence of optical pumping) prohibited the possibility of any phase relations between the initial atomic states. However, the concept of partial polarization or of an unpolarized state always refers to ensembles of individual quantum entities (like photons or atoms). The ensemble is unpolarized if its entities are uncorrelated, although each entity is always fully polarized (i.e., contains definite phase relations). The averaging must be done over the ensemble of Mueller matrices from the individual scattering processes. The definite (but random) phase relations between the initial ground states give non-zero contributions to the ensemble average when a phase closure condition with the final substates of the scattering process is satisfied. We show how the resulting, previously overlooked interference terms, can be included in a physically consistent way for any quantum system, and how these new effects provide an explanation of the decade-long D1 enigma from laboratory scattering at potassium gas, at the same time as explaining how a symmetric polarization peak can exist in the solar line of sodium D1.
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