Low temperature acoustic properties of amorphous silica and the Tunneling Model

Internal friction and speed of sound of a-SiO(2) was measured above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, non-linear effects, and clamping losses. Strain amplitudes e(A) = 10^{-8} mark the transition between the linear and non-linear regime. In the linear regime, excellent agreement with the Tunneling Model was observed for both the internal friction and speed of sound, with a cut-off energy of E(min) = 6.6 mK. In the non-linear regime, two different behaviors were observed. Above 10 mK the behavior was typical for non-linear harmonic oscillators, while below 10 mK a different behavior was found. Its origin is not understood.