Acoustic saturation in a glass at low temperatures

An experimental and theoretical study of nonlinear acoustic propagation in a typical glass, fused silica, is presented, at frequencies near 1 GHz and temperatures below 1 K. The data are interpreted within a general framework of pulse propagation in an inhomogeneously broadened two-level absorber. Numerical solutions are compared with the temperature and pulse-width dependence of the critical saturation intensity, as well as with saturation recovery experiments. The data are described by a linewidth $T_2^{-1\mathrm{}}$ of the intrinsic tunneling states that agrees with lifetimes obtained from phonon echo experiments. The distribution of relaxation times $T_1$ which emerges from the analysis of saturation recovery experiments is also understandable within the tunneling model. An improved estimate for the longitudinal deformation potential is ${\gamma }_L=2.0\mathrm{}$ eV. For $T<\mathrm{}0.1\mathrm{}$ K, the behavior of the pulse velocity is indicative of a coherent propagating mode, i.e., self-induced transparency.