FREQUENCY UP-CONVERSION IN INTERACTING PHONON BEAMS IN LIQUID ⁴He

Abstract

The interaction between intersecting phonon beams in liquid 4He has been studied as a function of pressure using superconducting A1 tunnel junction detectors. For pressures < 13 bar we detect high frequency phonons which are created by the annihilation of two lower frequency phonons. The critical frequency for this upconversion is well defined and is in good agreement with the value found from phonon decay via the 3 phonon process

Propagating phonons in liquid4He

“…If this signal is due to ballistic phonons, then the shape indicates that more phonons with w = 11 K are detected than ones with w = 10 K. It is unlikely that the injected spectrum increases with increasing energy in this range; so it appears that there is some attenuation of the phonons with energies just above w,. Such an attenuation can occur with scattering from the low density of ambient thermal phonons via the four-phonon process [21]. Although the thermal phonons are small and each scattering causes only a small change in energy of the large phonon, there can be many scatterings.…”

“…The result is a concentration of phonons at low w . For medium injected powers the density of phonons is high enough for there to be energy up-scattering by three-phonon processes [21] as well as decay. This pushes the spectrum to higher w .…”

Phonon propagation in liquid4He: the dependence on injected power and pressure

“…The density builds up and they interact through the three-phonon process, which produces up-conversion [23] as well as decay. The spectrum broadens and the tail extends to higher frequencies by an increasing amount as the power is increased.…”

“…At T = 0.25 K the signal shows two contributions, the faster one from w -2AA, phonons and the slower one from w > U, phonons. The resolution of the two contributions arises from the preferential attenuation of the phonons just above LO,, as these are most likely to scatter over the 0, edge [23]. By T = 0.3 K the only phonons that are left are those with w -2AA1 and they are spread out in time, probably by scattering.…”