Accurate measurement of low-energy phonon dispersion in liquid He4

This paper presents results of a new and highly accurate technique for measuring low-energy phonon dispersion in liquid He4. The technique is based on the behavior of ultrasonic second-harmonic generation in a lossless, dispersive medium. By using frequencies in the low gigahertz range and measuring second-harmonic intensity as a function of propagation distance, the coherence length for the harmonic generation can be determined. The coherence length is, in turn, related to the phonon dispersion curve in a simple way. The results are interpreted in terms of the series expansion μ(k)=c0k(1+1k+2k2+3k3+), where μ and k are phonon energy and wave number, respectively. By using measurements taken at two different fundamental frequencies, we find |±1|<10-3 at saturated vapor pressure (SVP) and 6.3 bars, and ±2=(1.56±0.06) 2 at SVP. If ±1 is assumed to be zero, the ±2 can be determined from a measurement at a single frequency, and we find ±2=(1.55±0.01) 2 at SVP. At higher pressures, ±2 decreases. Since the excitation spectrum is probed with such low-momentum phonons (k<0.011 -1), the analysis is insensitive to assumed values of ±4, ±5, etc., and is only slightly sensitive to the assumed value of ±3. © 1984 The American Physical Society.