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Physics of the Solid State

Optical dephasing in solid toluene activated by octaethylporphine zinc

Yu. G. Vainer, M. A. Kol’chenko, А. В. Наумов, Roman I. Personov, Stephan J. Zilker

Published Feb 1, 2003• 4 citations
Publisher

Abstract

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.

DOI
10.1134/1.1553521

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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.
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.
A study is made to analyze the possibility of using the soft-potential model in optical investigations of disordered molecular systems with impurities. A procedure is suggested for calculating the temperature dependence of the homogeneous width of a phononless line in amorphous media with impurities within the soft-potential model. A calculation is performed of the temperature dependence of the width of a phononless line (optical dephasing) in an amorphous system of polymethyl methacrylate (PMMA) with an addition of tetratert-butylterrylene (TBT) using the parameters of this system known from the literature. Calculations are performed of the contributions to the width of a phononless line due to the interaction of an impurity with tunneling two-level systems, with thermally activated barrier crossings in double-well potentials, and with quasilocal modes of the matrix. The model calculation results are compared with the experimental data on the photon echo for TBT/PMMA, measured by us in the temperature range from 0.3 to 20 K. It is found that the soft-potential model describes qualitatively correctly the temperature behavior of the homogeneous width of a phononless line. In the temperature range of T < 2 K, where the main contribution to optical dephasing is associated with tunneling two-level systems, the predicted values of phononless line width agree well with the experimental data. At higher temperatures, some difference is observed between the prediction and experimental data, which may be due to the effect of impurity on the formation of quasilocal oscillation of the matrix.
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.
The photon echo (PE) spectroscopy and single-molecule spectroscopy (SMS) may be combined to give a very powerful tool for comprehensive study of low-temperature dynamics in dye-doped disordered solids (polymers, glasses). At the same time, this type of studies are likely to reveal discrepancies when comparing characteristic times of optical dephasing T2 and single-molecule zero-phonon spectral lines (ZPL) broadening obtained from PE and SMS, correspondingly, for tetra-tert-butylterrylene in polyisobutylene in the temperature range of a few–dozen of Kelvins [see Phys. Status Solidi B 241, 3480 and 3487 (2004)]. Inexplicably, PE-experiments demonstrated T2-times to be much shorter than it is sufficient to cause the corresponding ZPL broadening. Here we experimentally solve this problem and show that at T = 4.5–15 K the incoherent PE gives T2-times which correspond to the narrowest SM ZPL. On the SM-level there is a pronounced additional ZPL-broadening due to spectral diffusion processes which are strongly dependent on the characteristics time of the measurement (tens of nanoseconds for PE and seconds for SMS). There is also a broad distribution of ZPL spectral widths for different SMs due to different local environments, that contribute differently to both the optical dephasing and the spectral diffusion processes, but always in addition to the value of inverse optical dephasing times measured using a PE technique.
The long-lived stimulated photon echo is put forward as a powerful technique to probe structural dynamics in glasses and other amorphous solids. We present results of optical dephasing measurements on several doped organic glasses (deuterated ethanol, toluene, and triethylamine) and polymers (polystyrene, polyvinylbutyral, and polymethylmethacrylate). Using a stochastic analysis within the so-called two-level-system model, we can extract from these measurements the distribution function of fluctuation rates over a huge range of time scales, varying from picoseconds to hundreds of milliseconds. We show that the dynamics, which lies at the origin of spectral diffusion, is very dependent on the glass structure and can be described by two separate hyperbolic distribution functions of fluctuation rates. From longitudinal photon echo measurements in the population dimension, we find evidence for structural dynamics which is not accounted for in the standard two-level-system model and which is related to a spatially inhomogeneous distribution of fluctuation centers.