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Application of averaging to spontaneous radiation processes for one-and two-atom systems, part one. A theoretical investigation of vibrational energy relaxation in solids, part two

Harold D. Ladouceur

Published Sep 1, 1978• 0 citations
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Recent theoretical and experimental work has shown that the simplest form of the Einstein equation relating induced absorption and spontaneous emission probabilities (characterized by Σ and τ−1) is not generally valid for impurities or color centers in solids, liquids, or molecules. Separate computations of these probabilities in systems exhibiting sizeable Stokes's shifts resolve some of the problems; they also disclose the difficulties involved in obtaining any connection between Σ and τ. Here we consider how the transition probabilities between a pair of electronic-vibrational states are related. Observable quantities, i.e., integrated absorption cross section and the radiative decay time, involve sums and averages over the vibrational states, and no definite theoretical information relates these quantities. However, there is a simple connection between induced and spontaneous emission probabilities. New experiments which could yield information about the rate of lattice relaxation are suggested from this point of view.
An investigation is made of the effect on the dynamics of spontaneous emission of the Wigner-Weisskopf atom in an infinite-system limit of various choices of the coupling function or form factor describing the atom's interaction with the spectrum of the radiation field. This is carried out both for the exact solution to the problem of spontaneous emission, obtained in the earlier papers in the series, and for some approximate solutions, also previously considered, in particular one based on the Schrödinger equation of the problem and one based on the weak-coupling Prigogine-Résibois master equation. The details of the form factor are found, by numerical computation of the solutions, to be critical in determining the nonexponential parts of the solutions, and these parts are seen to be capable in some cases of dominating the exponential parts, which are given only by the values of the form factor near the resonance energy. The approximate solutions discussed are found to vary widely in their worth, and one, which yields the exact solution for the Wigner-Weisskopf problem, is singled out as being of probable use in the statistical-mechanical description of more complicated systems.
Spontaneous ordering in a system of excited emitters with a powerful short radiation pulse predicted by Dicke attracted the great attention of scientists for decades as a bright example of the nontrivial behavior of a nonequilibrium system. The Bogolyubov reduced description method has some advantages and provides new possibilities in the theoretical investigation of the Dicke process. The paper presents the authors’ results of modeling such processes concerning both optical ones in the presence of crystal lattice influence and acoustic superradiance, which is possible in solids. The right choice of reduced description parameters allows the account of atom motions (phonons), cavity influence, and excitations in the emitter system (excitons) in the electromagnetic radiation process. The mathematical analogy between the Dicke system and a spin system in a magnetic field opens the way to applying the reduced description technique to acoustic phenomena previously investigated with the boson variable elimination method. Such a new approach to superradiance in crystals with paramagnetic impurities and with competing mechanisms of relaxation (Wagner model) is outlined. Acoustic superradiance is discussed in connection with the problem of structural phase transitions.