Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in ³ He-B

Abstract

Andreev reflection of quasiparticle excitations provides a sensitive and passive probe of flow in superfluid 3 He-B. It is particularly useful for studying complex flows generated by vortex rings and vortex tangles (quantum turbulence). We describe the reflection process and discuss the results of numerical simulations of Andreev reflection from vortex rings and from quantum turbulence. We present measurements of vortices generated by a vibrating grid resonator at very low temperatures. The Andreev reflection is measured using an array of vibrating wire sensors. At low grid velocities, ballistic vortex rings are produced. At higher grid velocities, the rings collide and reconnect to produce quantum turbulence. We discuss spatial correlations of the fluctuating vortex signals measured by the different sensor wires. These reveal detailed information about the formation of quantum turbulence and about the underlying vortex dynamics. Quantum turbulence in superfluid 4 He has been studied for many decades (3-5). There has been a great deal of renewed interest in quantum turbulence in recent years owing to several factors: quantum turbulence was discovered in superfluid 3 He (6-8), techniques were developed to extend the study of quantum turbulence in superfluid 4 He to very low temperatures (9, 10), imaging techniques were developed to visualize superfluid turbulence at higher temperatures (11-13) (see the review in ref. 14), mechanical resonator techniques were developed for quantum turbulence (15-18), and quantum turbulence was studied in dilute gases (19,20); there were many important theoretical developments, for example refs. 21-26, and numerical methods were enormously improved (27-29) to complement and better interpret experimental results.In this article, we discuss quantum turbulence generated by vibrating grids in superfluid 3 He-B at low temperatures, where the normal fluid component is very small. The primary thermal excitations in 3 He are quasiparticle and quasihole excitations (30). At low temperatures, the excitation mean free path between collisions vastly exceeds the experimental dimensions. In this ballistic regime, excitations move independently and normally scatter only with the container walls. The normal fluid concept no longer applies because there is no collective motion of excitations.In addition to normal scattering, excitations can also undergo Andreev reflection. Andreev scattering produces nearly perfect retroreflection of excitations with very little momentum transfer: Quasiparticles become quasiholes, and vice versa. This provides an ideal probe for vortices and quantum turbulence at low temperatures. Andreev Scattering from Superfluid FlowThe dispersion curve for excitations is shown in Fig. 1A. The excitation group velocity v g = dE=dp is parallel to the momentum for quasiparticles that have p > p F , where p F is the Fermi momentum and is antiparallel to the momentum for quasiholes that have p < p F . The dispersion curve is tied to the reference frame of the superfluid. So, accordi...

A Quasiparticle Detector for Imaging Quantum Turbulence in Superfluid $$^3$$ 3 He-B

“…The resulting vortices cast a quasiparticle shadow on the pixel which results in a reduction in the damping. The fractional reduction in damping is comparable to that observed in other types of measurements using vibrating wires [36,37,43,44].…”

“…This should be sufficient to gain useful information on the spatial profile of vortices generated by the wire as well as their dynamics. Calculations of Andreev reflection from vortices [37] show that under typical experimental conditions a single vortex in a quasiparticle beam will reflect around 2 % of the excitations over a distance of 0.5 mm either side of the core. Currently our measurement noise level is around 1 % so this is already sufficient to observe single vortex lines.…”

“…The spatial resolution is limited but it should be sufficient to gain useful information on the spatial profile of vortices generated by the wire as well as their dynamics. Based on calculations of Andreev reflection [37], we believe that the detector should be capable of detecting a single vortex line.…”

Quantum turbulence generated by oscillating structures

“…Vortex lines produced by the vibrating grid are detected, and their density measured, by a method involving the Andreev reflection of a low density of thermal quasiparticles from the superfluid velocity field; the quasiparticles are detected by their effect on the damping of two vibrating wire resonators (not shown in the figure). The method is described in detail in another article in this volume (40). At very small velocity amplitudes, it is probable that no vortex lines are produced by the grid.…”

“…The technique based on Andreev reflection of quasiparticles, applicable to 3 He-B and mentioned in the preceding section, provides some degree of visualization, but it has poor spatial resolution and is not easy to interpret (40,42). Methods based on a seeding of the flow with either micrometer-sized particles of solid hydrogen/deuterium or triplet-state He 2 excimer molecules are being successfully developed, as described in another article (43), and the former technique has revealed some strange flow patterns in the neighborhood of a solid cylinder immersed in a steady thermal counterflow in 4 He above 1 K. However, experiments with these hydrogen particles are hard to interpret because at high temperatures the particles undergo complicated interactions with both the normal fluid and the vortex lines, whereas loading is difficult at low temperatures.…”