A. F. G. Wyatt

Interactions between phonon sheets in superfluid helium

We have measured the effect of colliding two phonon sheets together at different angles. At small angles they interact strongly and a hot line is formed along the line of intersection of the two sheets. At angles between ~13? and ~27? the interaction becomes weaker and less energy goes into the hot line. At angles greater than ~27? there is no interaction between the sheets and they pass through each other. By delaying one sheet with respect to the other, the path of the hot line can be shifted laterally. Using this behaviour, we show that the sensitive area of the bolometer is around 10?2?mm2. We have measured the profile of the hot line and find that its width, typically 1?mm, varies as 1/sin(?/2), where ? is the angle between the two sheets. We analyse the data and estimate that the typical angle between two phonons interacting by the three phonon process varies between 8.4? and 12.5?, depending on their energy. We model the formation of the hot line when the sheets are strongly interacting. From the model and the measured data, we find that the temperature of the hot line decreases, and the cone angle and energy density of the hot line increases, with both increasing energy density in the sheets and increasing angle ?.

Evidence for a Bose-Einstein condensate in liquid 4He from quantum evaporation

Bose–Einstein condensation (BEC) is a purely quantum phenomenon whereby a macroscopic number of identical atoms occupy the same single-particle state. Interest in this phenomenon has grown considerably following the direct demonstration of BEC in low-density gases of alkali metal atoms. It is therefore worth reconsidering the case of liquid 4He, which is generally accepted to have such a condensate, but for which similarly direct evidence is lacking. Nevertheless, theoretical models that depend on the existence of a condensate have proved successful at explaining many of the properties of this system, and BEC is considered to underlie the striking phenomena of superfluidity and quantized vorticity observed in liquid 4He. So the current issue is not whether there is a condensate in this system, but how to demonstrate its existence in a clear and simple way. Here I argue that an earlier measurement of evaporation from liquid 4He caused by a collimated beam of phonons provides such a demonstration. The calculated angular distribution of evaporated atoms agrees well with that measured if it is assumed that the atoms initially had zero momentum parallel to the surface of the liquid—this is to be expected if the atoms originate from a condensate. This process of quantum evaporation also opens the possibility for creating beams of phase-coherent atoms of short wavelength.

The surface boundary conditions for quantum evaporation in 4He

Quantum evaporation of 4He atoms by phonons and rotons in liquid 4He is measured for a wide range of conditions. The results confirm that an atom is evaporated in a single-excitation to single-atom process and that the boundary conditions of conservation of energy and parallel momentum are obeyed. Excitations in the liquid are generated by pulse heating a thin metal film heater, and the evaporated atoms are detected by the energy yielded on condensation at the surface of a superconducting transition edge bolometer. The heater and bolometer can be rotated about a common axis in the liquid surface, and the collimation of the excitations and atoms into beams allows the angles of incidence and evaporation to be defined. It is first shown that the input power and pulse length must be carefully chosen to produce beams of phonons and rotons that are fully ballistic. The time of flight from the heater to the bolometer is measured, and the angular distribution of the evaporated atoms is determined for different angles of incidence. In particular, the wavevector dependence of the roton to atom pulse shape can be seen. The authors see no sign of Pitaevskii roton decay over the long liquid path lengths involved ( approximately 6 mm), and there is no indication that ripplons are created in the evaporation process.

Phonons in liquid 4He from a heated metal film. I. The creation of high-frequency phonons

For a very short (tp omega c( infinity )) are stable as T to 0. We find that for a heater power of 10 mW mm-2, these high-frequency phonons are not distributed over the available frequency range up to the maxon, but are concentrated in a narrow band around omega c( infinity ). Times of flight show that the distribution of high-frequency phonons depends upon pressure P such that the peak is always at the pressure dependent decay cut-off omega c( infinity )(P). We suggest that the majority of these detected high-frequency phonons are produced in the liquid 4He by frequency up scattering processes amongst the injected phonons.

Phonons in liquid 4He from a heated metal film. II. The angular distribution

For part I see ibid, vol.6, p.2813 (1994). We have measured the angular distribution of phonons emitted by an Au film heater in liquid 4He. For long heater pulses (10 mu s), the distribution is almost Lambertian ( alpha cos theta ), but for short pulses (0.1 mu s), the distribution is very anisotropic. The HWHM Of the beam of high-frequency (h(cross) omega /kB>10 K) phonons is approximately 3.5 degrees , and the HWHM Of the low-frequency (h(cross) omega /kB<1 K) phonon beam is approximately 10.5 degrees . We suggest that the angular distribution of the low-frequency phonons is due initially to classical phonon transmission at the heater/4He interface, but is then broadened by decays and interactions in the liquid. These interactions in the liquid create the high-frequency phonons. The high-frequency phonon beam is narrower than the low-frequency phonon beam due to momentum conservation in the four-phonon process (4PP) interactions that create them. Narrow beams of phonon emission from cleaved crystal surfaces have been observed before, but we believe that this is the first time that similarly narrow beams from evaporated metal surfaces have been observed.

Propagating phonons in liquid 4He

Phonon propagation in liquid 4He at T approximately=0.1 K is studied as a function of pressure input power and propagation distance. Using a superconducting tunnel junction detector it is found that a single injected pulse can form two propagating pulses at low pressures but only one at high pressures. It is shown that three-phonon scattering can explain this behaviour. At low pressures, one group of phonons propagates ballistically while another group consists of strongly interacting phonons which travel at the ultrasonic velocity.

SPATIAL EVOLUTION OF HIGH FREQUENCY PHONONS IN SUPERFLUID 4HE FROM A PULSE-HEATED METAL FILM

An almost monochromatic spectrum of high frequency (ħω/kB∼ 10 K) phonons in superfluid4He is created by a short (∼ 0.1μs) pulse of Joule-heating in a metal film submerged in the liquid at saturated vapour pressure (svp). These phonons have lifetimes that tend to infinity as T → 0, and are the ones effective in quantum evaporation experiments. Most of these high frequency (hf) phonons are not injected into the liquid4He across the metal—liquid interface, but are created in the liquid by energy-increasing interactions which begin with the injected phonons of much lower energy (ħω/kB∼ 1 K). These hf phonons are created up to ∼ 5 millimetres in front of the heater, hence the time of flight from a heater to a detector only gives an approximate value (lower bound) of their energies. Here we present measurements at svp of phonon energy fluxes in liquid4He at various distances from a pulse-heated metal film. Analysis of these signals gives an improved determination of the hf phonon spectrum (peaked at 10.20 ± 0.05 K with HWHM ≃ 0.2 K on the high energy side).

Four-phonon scattering in superfluid 4He

The scattering of high-frequency (h(cross) omega /kB>10 K) phonons injected into superfluid 4He with low-frequency (h(cross) omega /kB<1 K) thermal phonons in the liquid is studied both experimentally and theoretically. Quantum evaporation enables the selective study of only the high-frequency phonons. The attenuation of evaporation signals as the temperature is increased from 70 mK to 250 mK for various liquid path lengths is interpreted in terms of four-phonon scattering involving the high-frequency injected phonons and the low-frequency thermal phonons. Monte Carlo simulations of the signal variation with temperature show that the measured scattering is much weaker than the hydrodynamic theory has previously predicted. However, when this theory is extended to include diagrams representing further possible routes of the four-phonon scattering process, there are significant cancellations between these extra diagrams and those considered earlier. This leads to a weaker interaction and to a much improved agreement with the experimental results.

Three-phonon relaxation in isotropic and anisotropic phonon systems of liquid helium at different pressures

Starting from the kinetic equation for phonons in superfluid helium, expressions for the rates of three-phonon scattering in isotropic and anisotropic phonon systems are obtained for different pressures. These expressions are valid in the whole range of energies where three-phonon processes are allowed. Limiting cases are analyzed and compared with the results of previous theoretical investigations. The obtained pressure and angular dependence of three phonon scattering rate allows one to explain the experimental data on interaction of phonon pulses.

Three-phonon interactions and initial stage of phonon pulse evolution in He II

An expression for the characteristic rate of three-phonon processes in superfluid 4He, which is valid in the entire range of phonon energies where three-phonon processes are allowed is derived proceeding from the hydrodynamic Landau Hamiltonian. Possible limiting cases are analyzed and compared with the results of previous investigations. It is found that three-phonon processes completely govern the initial relaxation of a phonon pulse injected into He II by a heated solid. As a result, the equilibrium form of phonon distribution is established in the anomalous region of phonon dispersion over a time interval of the order of 10−10 s.