Nonperturbative theory of temperature-dependent optical dephasing in crystals. II. Pseudolocal phonons

Abstract

We continue our discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In Paper I of this series we evaluated our general results for the linewidth and shift for models of electronic coupling to both acoustic and optical phonons. Here we evaluate our general results for a simple model of electronic coupling to a pseudolocal phonon. The pseudolocal phonon is characterized by its frequency and lifetime in both the ground and excited electronic states. In addition to providing exact analytic expressions (reduced to quadrature) for the width and shift, we derive an approximate analytic expression for the linewidth that is bi-Arrhenius, with activation energies corresponding to the ground and excited state pseudolocal phonon frequencies. We discuss how our theoretical approach and results are related to the exchange theory of Harris, the optical Redfield theory of deBree and Wiersma, and the perturbation theory of Small and Jones and Zewail. In Paper III of this series, we compare the results of this paper and of Paper I to experiment.

Theory of Pure Dephasing in Crystals

“…This again provides a no-free-parameter test of the theory, and again the results are quite satisfactory. Both of these last two systems have also been analyzed with our phenomenological model (12) with similar results (13,43). Another approach to the analysis of experi mental systems with pseudolocal modes is to use our low temperature result of Eq.…”

“…Finally, as an approach to dephasing from pseudolocal modes, one can describe r o(ro) phenomenologically by a Lorentzian (2, 3, 12, 40). This leads (12) to results that are completely equivalent to the fast exchange limit of Harris' theory (3Ia,b).…”

“…We have also examined the dephasing by pseudolocal modes with a more phenomenological model (12), simply choosing r o(w) to be a par ticular sharply peaked function, rather than deriving its form from a microscopic Hamiltonian. Again, however, we have derived Eq.…”

“…They have also been used to describe dephasing by optical phonons, again by setting V = 0 and taking r o( w) = r p( w), where r pC w) can be modeled (for example) by Eq. 18 (3,12,40). Finally, as an approach to dephasing from pseudolocal modes, one can describe r o(ro) phenomenologically by a Lorentzian (2, 3, 12, 40).…”

Structural relaxations in disordered solids below Tg: Study by thermal-cycling single-molecule spectroscopy

“…The quadratic coupling of a SM to a LFM leads to homogeneous broadening of the SM spectrum by the amount [22,[33][34][35][36] …”