Visualizing Pure Quantum Turbulence in Superfluid ${}^3\mathrm{He}$: Andreev Reflection and its Spectral Properties

Superfluid ${}^3\mathrm{He}\text{−}\mathrm{B}$ in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in ${}^3\mathrm{He}\text{−}\mathrm{B}$ by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the intervortex separation.

Figure 1

A 2D representation of the reflection coefficient of excitations incident on one side of the calculation cell. Left: quasiparticle reflection. Right: quasihole reflection. The vortex cores are clearly visible as the dark lines. The extended regions of high reflectivity (darker) and low reflectivity (lighter) illustrate the distribution of the large-scale flows in the cell.

Figure 2

Top: the total reflection coefficient obtained from the numerical simulations, plotted against the line density of the vortex tangle. Bottom: experimental measurements of the fraction of Andreev scattering from vortices generated by a grid plotted versus grid’s velocity. Measurements are shown for three vibrating wires at different distances from the grid as shown in the inset, see text.

Figure 3

Power spectral density of the Andreev reflection for numerical simulations (top, blue) and experimental observations (middle and bottom, gray) versus frequency. For the details, see text.

Figure 4

Power spectral densities of simulated Andreev reflection (bottom, blue) and of simulated vortex line density (top, red) versus frequency. Note that the accuracy of the initially calculated line density PSD extends to higher frequencies than the Andreev-reflection PSD derived from it. Inset: cross-correlation between the Andreev reflection coefficient and vortex line density. The central peak reaches a value of 0.9.