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The Journal of Chemical Physics

Nonperturbative theory of temperature-dependent optical dephasing in crystals. III. Comparison with experiment

David Hsu, James L. Skinner

Published Sep 1, 1985• 48 citations
Publisher

Abstract

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.

DOI
10.1063/1.449353

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We have performed optical photon echo measurements on amorphous toluene doped with zinc-octaethylporphine over a wide temperature interval (0.35–100 K). This broad temperature range, reaching from subkelvins up to the Debye temperature of toluene (100.7 K), enabled a clear separation between the low and high temperature contributions of line broadening processes to the total optical dephasing. The high temperature part of the measured dephasing times was analyzed using recent data from light scattering experiments which determined the spectrum of low-frequency modes of the toluene matrix. The analysis shows that two line-broadening mechanisms contribute mainly to total dephasing: the tunneling transitions of two-level systems, which lead to a power-law temperature dependence of the linewidth at low temperatures (T<3–4 K), and the interaction of the chromophore with low-frequency phonon modes of the glassy matrix, which gives rise to an exponential behavior at high temperatures. It was shown that the contribution of acoustic phonons to optical dephasing in the studied system is negligible over the whole temperature region of the measurements.

The Journal of Chemical Physics•May 22, 2002•11 citations
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 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 present a nonperturbative theory of the thermal line broadening of optical transitions due to pure dephasing by phonons. The theory extends previous perturbative results of McCumber and Sturge. The theory is applied to experimental results on mixed organic crystals and ruby. We also present a theory of dephasing at T=0 K due to interacting impurities. Our results predict a frequency dependence to 1/T2. We analyze experiments on Y2O3:Eu3+ by Macfarlane and Shelby with this theory, and are able to comment on the nature of inhomogeneous broadening in this system.
The first two-pulse photon echo experiments on a chromophore in an organic glass are reported. The homogeneous electronic dephasing of resorufin in ethanol glass is measured from 1.5–11.4 K. The temperature dependence of the dephasing time does not fit the power law frequently predicted by theory for the dephasing characteristic of glasses. However, the temperature dependence can be accounted for by including dephasing from librations or acoustic phonons, mechanisms known to be important in crystals. The dephasing decay is found to be a single exponential for over six factors of e. The dephasing is also shown to be uncorrelated with the extent of nonphotochemical hole burning (NPHB). However, the homogeneous linewidth deduced from the photon echo is four times narrower than the linewidth obtained from NPHB, demonstrating that the hole is broadened by additional processes.
The optical dephasing in frozen amorphous toluene doped with octaethylporphine zinc is investigated using the photon echo technique over a wide range of temperatures (0.4–100 K) up to the Debye temperature of solid toluene (T D=100.7 K). The contributions of different mechanisms to the broadening of the zero-phonon line (ZPL) are reliably separated owing to the measurements performed over such a wide range of temperatures. Analysis of the experimental data demonstrates that, at low temperatures, the main contribution to the optical dephasing is determined by the interaction of impurities with fast tunneling transitions in two-level systems. The temperature dependence of the linewidth exhibits a quasi-linear behavior at temperatures below 3–4 K. At higher temperatures, the dominant contribution to the dephasing is made by the interaction of impurities with quasi-local phonons, which leads to a quasi-exponential temperature dependence of the linewidth. It is shown that the latter contribution can be described in the framework of the soft-potential model allowing for a broad spectrum of low-frequency phonon vibrations in the matrix. The temperature of the crossover between the aforementioned two mechanisms of line broadening is determined.
The temperature-dependent optical dephasing of anthracene, 9-methylanthracene, and 2-methylanthracene monomers in phenanthrene host crystals has been measured using photon echo experiments. Despite large linear electron–acoustic phonon coupling, all three systems dephase because of coupling to pseudolocal modes (local motions of the guest molecule). Computer simulations of the three systems calculate the pseudolocal mode eigenvalues and eigenvectors. In contrast to previous discussions in the literature which describe pseudolocal modes as librations, the predicted eigenvalues are in reasonable agreement with the measured pseudolocal mode energies. The predicted eigenvectors are combinations of translational motion along the long molecular axis and rotational motion about the out-of-plane axis of the guest. Differences in site energies for various locations and orientations of the methyl group are calculated.
We have performed optical photon echo measurements on amorphous toluene doped with zinc-octaethylporphine over a wide temperature interval (0.35–100 K). This broad temperature range, reaching from subkelvins up to the Debye temperature of toluene (100.7 K), enabled a clear separation between the low and high temperature contributions of line broadening processes to the total optical dephasing. The high temperature part of the measured dephasing times was analyzed using recent data from light scattering experiments which determined the spectrum of low-frequency modes of the toluene matrix. The analysis shows that two line-broadening mechanisms contribute mainly to total dephasing: the tunneling transitions of two-level systems, which lead to a power-law temperature dependence of the linewidth at low temperatures (T<3–4 K), and the interaction of the chromophore with low-frequency phonon modes of the glassy matrix, which gives rise to an exponential behavior at high temperatures. It was shown that the contribution of acoustic phonons to optical dephasing in the studied system is negligible over the whole temperature region of the measurements.