No abstract

We examine the problem of the absorption zero-phonon line shape for dilute impurities in crystals. We consider the usual two level electronic model, where both the ground and excited state Born–Oppenheimer surfaces are harmonic in the phonon coordinates. The difference between the two surfaces (the electron–phonon interaction) has terms which are both linear and quadratic in the phonon coordinates. In contrast to the usual perturbative theories, we calculate the zero–phonon line broadening and shift to all orders in the electron–phonon interaction. We find that only the quadratic term is responsible for line broadening, and that at T=0 K this contribution vanishes. Our results are presented as integrals, which can be performed analytically or numerically, involving the weighted phonon density of states. We also show that within the model, the zero-phonon lines in the absorption and fluorescence spectra coincide exactly for all temperatures. Our results resolve the theoretical controversy produced by the two previous attempts to solve the line shape problem for strongly coupled electron–phonon systems. The work by Osad’ko is shown to be correct.

We continue the discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero-phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo-local phonons, and in paper III we will compare our results to absorption, photon echo, and hole burning experiments.

We have applied the results of the nonperturbative theory of zero-phonon linewidths of impurities in crystals discussed by Osad’ko and us, and further developed by us in papers I and II of this series, to the analysis of several absorption, photon echo, and hole burning experiments. Two (relatively) high temperature absorption experiments on 1,3-diazaazulene in naphthalene and dilute ruby were analyzed with a model of Debye acoustic phonons. In both cases the Debye temperature was obtained from independent experiment or theory, and a one-parameter fit was performed on the temperature-dependent linewidth. It was found that (especially for diazaazulene) the systems are not in the weak coupling limit. For several low temperature experiments, where the dephasing is presumably due to pseudolocal phonons, the nonperturbative theory, coupled with the results of deBree and Wiersma, provides a reasonably complete understanding of the observed dephasing rates.

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.