Interactions between Sheets of Phonons in Liquid ${}^4\mathrm{H}\mathrm{e}$

We have created two sheets of $\sim 1\mathrm{K}$ phonons in liquid ${}^4\mathrm{H}\mathrm{e}$ at $\sim 55\mathrm{m}\mathrm{K}$ such that they intersect each other as they move towards a common point. If the two sheets have a small angle between them, they interact strongly and create a hot line in the liquid helium. This line is continuously fed with energy from the two sheets and loses energy by creating high-energy phonons. If the angle between the sheets is larger than $\sim 30°$ they do not interact but pass through each other. These results give direct evidence for the composition of the sheets: they comprise strongly interacting low-energy phonons which occupy a narrow cone in momentum space.

Figure 1

This shows the bolometer signals for the two separate pulses (dash-dotted lines) and for the double pulse (solid line). The sharp peak at $41\mu \mathrm{s}$ is due to the l phonons; the signal after $\approx 44\mu \mathrm{s}$ is due to the h phonons. The sum of the signals from the two separate pulses is shown as the dotted line; it can be seen to be about half that of the double pulse. The input pulses are 100 ns and 6.3 mW.

Figure 2

For heaters with a $6°$ angle between them, the ratio of the integrated signals from the double pulse to the sum of the integrated signals from the separate pulses is shown as a function of heater power (the reference power is 0.5 W, so $-22$, $-19$, $-16$, and $-13\mathrm{d}\mathrm{B}$ correspond to 3.1, 6.3, 12.5, and 25 mW, respectively). The curves labeled l, ${\mathrm{h}}^{\prime }$, h, and ${\mathrm{h}}^{\prime \prime }$ are integrated over time intervals 40–43, 43–50.4, 43–73, and $50.4–73\mu \mathrm{s}$, respectively. The time $50.4\mu \mathrm{s}$ is the propagation time for the fastest h phonon which has energy $ϵ=10\mathrm{K}$. The pulse durations are 100 ns.

Figure 3

(a) A schematic of the phonon sheet moving in the $z$ direction. (b) The cone in momentum space occupied by the phonons in the sheet. (c) Two phonon sheets at a small angle to each other; the normals to the two sheets are indicated. (d) The overlap of the two cones in momentum space is shown. (e) Two phonon sheets with a large angle between them. Note that the sheets pass through each other. (f) The two occupied cones separated. (g) A plan view of the two phonon sheets at different times. The sheets are created at time $t_1$, and at $t_2$ they start to touch and begin to create the hot line. For $t>t_2$ the area of the sheets decrease and their energy is fed into the hot line. The h phonons, created by the hot line, trail behind the two phonon sheets, but are not shown.

Figure 4

For heaters with an angle $\alpha$ between them of $26°$, the ratio $R$ of the integrated signals from the double pulse to the sum of the integrated signals from the separate pulses is shown as a function of heater power (the reference power is 0.5 W, so $-22$, $-19$, $-16$, and $-13\mathrm{d}\mathrm{B}$ correspond to 3.1, 6.3, 12.5, and 25 mW, respectively). The curves labeled l, ${\mathrm{h}}^{\prime }$, h, ${\mathrm{h}}^{\prime \prime }$ are integrated over time intervals 40–43, 43–50.4, 43–73, and $50.4–73\mu \mathrm{s}$, respectively. The pulse durations are 100 ns.