Phonon echoes in a glass at low temperatures

Abstract

Coherent acoustic echoes are generated in fused silica glass at very low temperatures by a sequence of short acoustic pulses that interact with the intrinsic two-level configurational systems of the glass. Coherent effects are observable below $T\approx 100$ mK, where the two-level-system phase memory time ${T^{\prime }}_2$ is long compared to the acoustic pulse length, typically 100 nsec. The dependence of spontaneous (two-pulse) and stimulated (three-pulse) echo amplitude on the amplitude, width, frequency, and separation time of the generating pulses has been studied in the frequency range 0.7-1.5 GHz and at temperatures of 18-80 mK. The area of the generating pulses is shown to be the relevant descriptive parameter. The value of the area that produces maximum echo amplitude is used to deduce the average value of the deformation potential ${\gamma }_L$ which couples a two-level system and a longitudinal acoustic wave, with the result ${\gamma }_L=1.5\mathrm{}\pm 0.4$ eV. The two-pulse echo decay time is 16 μsec at 18 mK and varies as $T^{-2\mathrm{}}$. This behavior may be understood in terms of spectral diffusion arising from elastic dipolar interactions between resonant and nonresonant two-level systems. The three-pulse echo decay is not exponential, but may be characterized by an initial decay time of 100 μsec at 0.7 GHz and 18 mK. This is in reasonable agreement with a direct-process thermal equilibration time $T_1$ calculated from the present value of ${\gamma }_L$. At higher temperatures, the decay rate is faster than indicated by the direct process, and may be understood semiquantitatively in terms of spectral diffusion.