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 and the homogeneous linewidth as
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.
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.