Theory of single-molecule optical line-shape distributions in low-temperature glasses

We present a theoretical framework for analyzing the distribution of optical line shapes in low-temperature glasses, as measured by single-molecule spectroscopy. The theory is based on the standard tunneling two-level system model of low-temperature glasses and on the stochastic sudden jump model for the two-level system dynamics, Within this framework we present an explicit formula for the line shape of a single molecule and employ Monte Carlo simulation techniques to calculate the distribution of single-molecule line shapes. We compare our calculated line-width distributions to those measured experimentally. We find that the two-level system model captures the features of the experimental line-width distributions very well, although there are discrepancies for small line widths. We also discuss the relation of single-molecule line-shape distributions to more traditional ''line shapes'', as measured by hole-burning and photon echo spectroscopies. Using the results from our analysis of the single-molecule line-width distributions, with no adjustable parameters we can compare theoretical predictions with experiment for photon echo decay times and hole widths. In general, the agreement is good, providing further evidence that the standard tunneling model in glasses is basically correct. For two systems, however, theory and experiment do not agree quantitatively.