Observation of quantum turbulence in superfluid ${}^3\mathrm{He}$-B using reflection and transmission of ballistic thermal excitations

We report measurements of quantum turbulence generated by a vibrating grid in superfluid ${}^3\mathrm{He}$-B at zero pressure in the zero temperature limit. Superfluid flow around individual vortex lines Andreev reflects incoming thermal ballistic quasiparticle excitations, and allows noninvasive detection of quantum vortices in ${}^3\mathrm{He}$-B. We have compared two Andreev reflection-based techniques traditionally used to detect quantum turbulence in the ballistic regime: quasiparticle transmission through and reflection from ballistic vortex rings and a turbulent tangle. We have shown that the two methods are in very good agreement and thus complement each other. Our measurements reveal that vortex rings and a tangle generated by a vibrating grid have a much larger spatial extent than previously realized. Furthermore, we find that a vortex tangle can either pass through an obstacle made from a mesh or diffuse around it. The measured dependence of vortex signal as a function of the distance from the vibrating grid is consistent with a power-law behavior in contrast to turbulence generated by a vibrating wire which is described by an exponential function.

Figure 1

Schematic diagram of the experimental volume showing the mechanical oscillators used in our measurements. For details, see text.

Figure 2

Logarithmic-linear plot of the fractional screening measured by the four wire detectors as a function of the peak grid velocity at zero pressure over the temperature range $0.17T_c–0.19T_c$. The vertical dashed line shows the approximate grid velocity where vortex rings entangle and produce quantum turbulence. The insert contrasts a representation of 10-$\mu \mathrm{m}$ diameter vortex rings and a micrograph of grid 2, which separates wire 4 from the source of turbulence and other detectors. See text for details.

Figure 3

The normalized fractional screening, averaged over a range of grid velocities, as a function of distance from the grid. The solid and dashed lines correspond to least-square fitting of normalized fractional screening measured by wires 1, 2, and 3 using exponential and power-law functions, respectively. The cyan filled circle shows the expected response of wire 4 in the absence of grid 2, whose location is shown as the vertical dashed line. See text for details.

Figure 4

Change of width parameter $\delta \mathrm{\Delta }{f}_2^T{\tilde{E}}_{T}T$ for both BBRs as a function of applied power, where $T$ and ${\tilde{E}}_T$ are in units of milidegrees Kelvin using the Greywall temperature scale [30]. The open and closed symbols correspond to the change of width parameter of the heated (under calibration) and unheated (receiving beam from the heated box) BBRs correspondingly. The heat leak from the walls into the BBR, ${\dot{Q}}_{\mathrm{wall}}$, is estimated to be $\le 25$ fW. The straight solid line is least-squares fit with a gradient of unity, which yields the box calibration constant $c=85\mathrm{Hz}{\mathrm{mK}}^2{\mathrm{pW}}^{-1}$. The dashed line corresponds to the expected fraction of the received quasiparticle beam, and agrees very well with measurements. For details, see text.

Figure 5

Comparison of turbulence measurements using reflection and transmission techniques during a typical grid pulse. The light grey area corresponds to the time when the grid is switched on and produces turbulence. The grid velocity is 5.6 mm ${\mathrm{s}}^{-1}$. (a) Width parameter of heated BBR. (b) Width parameters of unheated BBR and the bulk thermometer. (c) The variation of applied power ${\dot{Q}}_{\mathrm{app}}$ during the creation of turbulence. (d) Change of damping experienced by the bulk thermometer and detector wires 2 and 4. (e) Fractional screening measured by reflection (BBR) and transmission (wires 2 and 4) techniques during a grid pulse.

Figure 6

Comparison of fractional screening measured using transmission (wire 4) and reflection (BBR) techniques as a function of the grid's velocity. Both data sets are in very good agreement. The right axis shows the approximate vortex line densities inferred using a simple 1D model which assumes that the tangle is homogeneous using Eq. (11) from Ref. [9]. For the details, see text.