Mutual friction in superfluid $^3$He-B in the low-temperature regime

TL;DR

This study investigates the mutual friction in superfluid helium-3 B at very low temperatures, revealing how vortex dynamics and surface excitations influence dissipation and align with theoretical models.

Contribution

It provides the first detailed measurement of mutual friction parameter $oldsymbol{eta}$ in superfluid helium-3 B at near-zero temperatures, confirming theoretical predictions and identifying a pressure-independent residual dissipation.

Findings

Mutual friction parameter $oldsymbol{eta}$ matches theoretical temperature and pressure dependence.

Residual dissipation at zero temperature is approximately $5 imes 10^{-4}$, independent of pressure.

Surface-induced Kelvin waves contribute to energy dissipation in the superfluid.

Abstract

We measure the response of a rotating sample of superfluid $^3$He-B to spin-down to rest in the zero-temperature limit. Deviations from perfect cylindrical symmetry in the flow environment cause the initial response to become turbulent. The remaining high polarization of vortices along the rotation axis suppresses the turbulent behavior and leads to laminar late-time response. We determine the dissipation during laminar decay at $(0.13-0.22) T_{\mathrm{c}}$ from the precession frequency of the remnant vortex cluster. We extract the mutual friction parameter $\alpha$ and confirm that its dependence on temperature and pressure agrees with theoretical predictions. We find that the zero-temperature extrapolation of $\alpha$ has pressure-independent value $\alpha(T=0) \sim 5 \cdot 10^{-4}$, which we attribute to a process where Kelvin waves, excited at surfaces of the container, propagate into the bulk and enhance energy dissipation via overheating vortex core-bound fermions.