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 ?.

http://iopscience.iop.org/article/10.1088/1367-2630/8/8/128/pdf

Interactions between phonon sheets in superfluid helium

We study the interactions among phonons and the phonon lifetime in a pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime. To compute the phonon-phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC-BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev-Landau process 2 phonons $\leftrightarrow$ 1 phonon while, when the concavity is downwards, it is the Landau-Khalatnikov process 2 phonons $\leftrightarrow$ 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF {\bf 19}, 637 (1949)] for the $2\leftrightarrow2$ processes in the downward concavity case. In the upward concavity case, for the Beliaev 1$\leftrightarrow$ 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number $q$ including the first correction proportional to $q^7$ to the $q^5$ hydrodynamic prediction, which was never done before in a systematic way.

Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas

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. I. The creation of high-frequency phonons

We present experimental results on the condensation of 4He atoms on the surface of liquid 4He. We show that there is quantum condensation with the creation of phonons and R+rotons in one-to-one processes as atoms go into the Bose–Einstein condensate. These phonon and R+roton signals can be recognized by their time of flight, their angular distribution and their dependence on the ambient temperature. Condensing atoms also create ripplons with a high probability. We derive rate equations for the growth of the ripplon density and the ripplon decay by the creation of bulk phonons. During the atom pulse a dynamic equilibrium is established. The low-energy phonons that are created by ripplon–ripplon scattering can easily be detected and distinguished from the phonons created by quantum condensation.From measured data, estimates are made of the probabilities of creating phonons, R+rotons and ripplons in condensation processes as well as estimates of the quantum evaporation probabilities of phonons and rotons.We clearly detect R+rotons directly with a bolometer in the liquid 4He and show why the signal of R+rotons is obscured by the low-energy phonon signal when both the source and detector are in the liquid helium. Values of the Kapitza conductance for the Zn bolometers are derived.

Quantum condensation of liquid 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.

http://iopscience.iop.org/article/10.1088/0953-8984/4/38/008/pdf

M A H Tucker

Papers

Four-phonon scattering in superfluid 4He