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The Journal of Physical Chemistry B

Modified Model of Photon Echoes in Low-Temperature Glasses: Effect of Minimal Distance between Two-Level Systems and Chromophore

А. В. Наумов, Yuri G. Vainer

Published Feb 6, 2003• 1 citation
Publisher

Abstract

A modified theoretical model of photon echoes (PE) in low-temperature doped glasses based on the tunneling two-level system (TLS) and stochastic sudden jump models has been developed. The distinguishing feature of the model is its adaptation for Monte Carlo technique. The developed approach is more general than usual PE theories and allows us to take into account the different microscopic parameters of spectral dynamics in doped amorphous solids: in particular, the minimal radius of interaction between TLS and chromophore molecules, the dispersion of this coupling constant, and the changes of matrix properties nearby chromophore (shell-effect). The developed theory was applied for calculations of two-pulse PE decays for an organic amorphous system with typical parameters. It was found that the slope of temperature dependence of the homogeneous line width is decreased with an increase in the above-mentioned minimal radius. This effect could be one of the main reasons for the discrepancy between some PE experimental results versus calculation using standard PE theory.

DOI
10.1021/jp022146l

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A modified theoretical model of photon echoes (PE) in low-temperature doped glasses based on the tunneling two-level system (TLS) and stochastic sudden jump models has been developed. The distinguishing feature of the model is its adaptation for Monte Carlo technique. The developed approach is more general than usual PE theories and allows us to take into account the different microscopic parameters of spectral dynamics in doped amorphous solids: in particular, the minimal radius of interaction between TLS and chromophore molecules, the dispersion of this coupling constant, and the changes of matrix properties nearby chromophore (shell-effect). The developed theory was applied for calculations of two-pulse PE decays for an organic amorphous system with typical parameters. It was found that the slope of temperature dependence of the homogeneous line width is decreased with an increase in the above-mentioned minimal radius. This effect could be one of the main reasons for the discrepancy between some PE experimental results versus calculation using standard PE theory.
The effect of high pressure on the optical dephasing of chromophores in organic polymers at low temperature is evaluated within the stochastic sudden jump two-level-system (TLS) model. The approximations within the "standard" TLS model cannot account for the observed pressure dependence of the pure dephasing rate without ad hoc assumptions about changes in the TLS density of states. However, the photon echo model of Geva and Skinner for disordered systems can be used to model pressure-dependent optical dephasing results for a variety of doped polymer systems without assuming changes in the TLS density of states. The relative importance of pressure-induced changes in TLS density, chromophore-TLS coupling, and TLS-phonon coupling is evaluated by fitting experimental high-pressure photon echo results to the TLS model.
The theory of optical photon echo and hole burning spectroscopies in low temperature glasses is discussed within the framework of the tunneling two-level system and stochastic sudden jump models. Exact results for the relevant theoretical quantities involve certain averages over the distributions of the two-level system energies and relaxation rates. The standard approximations for these averages are critically examined, for experimentally realistic parameters, via comparison to numerically exact calculations. The general conclusion is that the standard approximations are often used under conditions where they are not expected to be quantitatively accurate.
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.
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Using a stochastic model, we calculate the temperature dependence of the homogeneous linewidth and the two-pulse photon-echo decay rate of optically active impurities in glasses. The theory applies to the low-temperature regime T\ensuremath{\lesssim}10 K, where it is assumed that the dephasing arises from an elastic dipole interaction of the impurity with an array of thermally excited tunneling systems. Averaging over the tunneling parameters and using relaxation rates appropriate to vitreous silica, we find that the photon-echo decay rate varies as T1.1{T}^{1.1}T1.1 and the homogeneous linewidth as T1.2{T}^{1.2}T1.2 for 0.1\ensuremath{\le}T\ensuremath{\le}1 K, assuming a constant density of states for the tunneling systems. Both the photon-echo amplitude and the optical dipole-moment correlation function decay exponentially in time. The rates, however, are different, with a ratio of photon-echo dephasing time to optical-absorption dephasing time of 6.9 at T=1 K, assuming a constant density of states. The relation of our results to various experimental studies is discussed.
Until now, in spite of a great number of experimental and theoretical works in study of organic amorphous solids, the basic features of the low temperature dynamics of these mediums are poorly understood. One of the main reason of this is the lack of experimental information about these dynamical processes. In particular, it’s necessary to learn more about optical dephasing in doped organic glasses and polymers for wider temperature interval. It will allow to test the existent theories more correctly and to create new conceptions.