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arXiv:1708.05579 · Astronomy and Astrophysics

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit

V. Bommier

Published Aug 18, 2017• 25 citations
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Abstract

Context. In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution).
DOI
10.1051/0004-6361/201630169

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We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
A study is undertaken to cast light on difficulties, which arose in the first two papers of this series, pertaining to the occurrence of negative probabilities in the weak-coupling solution of the generalized Prigogine-Résibois master equation for the model of the Wigner-Weisskopf atom in a one-dimensional radiation field. The Schrödinger equation is solved exactly for the model with the initial condition for spontaneous emission, and then the weak-coupling approximations to the solution, both for an infinite and for a finite system, are derived as inverse Laplace transform integrals. An extensive analysis, theoretical and numerical, of these is undertaken, and comparison is made with the corresponding results based on the master equation. In particular, quantitative estimates of the Poincaré recurrence times for finite systems are made. It is found that considerable differences exist between the statistical-mechanical and quantum-mechanical results, but that both manifest nonanalyticity in the coupling parameter as it tends to zero. Suggestions are given for further work toward the resolution of these discrepancies and a better understanding of the weak-coupling limit.