Andreev reflection of quasiparticle excitations from quantized line vortices is reviewed in the isotropic B phase of superfluid $^3$He in the temperature regime of ballistic quasiparticle transport at $T leq 0.20,T_mathrm{c}$. The reflection from an
array of rectilinear vortices in solid-body rotation is measured with a quasiparticle beam illuminating the array mainly in the orientation along the rotation axis. The result is in agreement with the calculated Andreev reflection. The Andreev signal is also used to analyze the spin down of the superfluid component after a sudden impulsive stop of rotation from an equilibrium vortex state. In a measuring setup where the rotating cylinder has a rough bottom surface, annihilation of the vortices proceeds via a leading rapid turbulent burst followed by a trailing slow laminar decay from which the mutual friction dissipation can be determined. In contrast to currently accepted theory, mutual friction is found to have a finite value in the zero temperature limit: $alpha (T rightarrow 0) = (5 pm 0.5) cdot 10^{-4}$.
In a rotating two-phase sample of 3He-B and magnetic-field stabilized 3He-A the large difference in mutual friction dissipation at 0.20 Tc gives rise to unusual vortex flow responses. We use noninvasive NMR techniques to monitor spin down and spin up
of the B-phase superfluid component to a sudden change in the rotation velocity. Compared to measurements at low field with no A-phase, where these responses are laminar in cylindrically symmetric flow, spin down with vortices extending across the AB interface is found to be faster, indicating enhanced dissipation from turbulence. Spin up in turn is slower, owing to rapid annihilation of remanent vortices before the rotation increase. As confirmed by both our NMR signal analysis and vortex filament calculations, these observations are explained by the additional force acting on the B-phase vortex ends at the AB interface.
Steady-state turbulent motion is created in superfluid 3He-B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of 3He-B and replaces vortex-free flow with vortex lines at constant
density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2 Tc during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e. the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.
Vortex flow remains laminar up to large Reynolds numbers (Re~1000) in a cylinder filled with 3He-B. This is inferred from NMR measurements and numerical vortex filament calculations where we study the spin up and spin down responses of the superfluid
component, after a sudden change in rotation velocity. In normal fluids and in superfluid 4He these responses are turbulent. In 3He-B the vortex core radius is much larger which reduces both surface pinning and vortex reconnections, the phenomena, which enhance vortex bending and the creation of turbulent tangles. Thus the origin for the greater stability of vortex flow in 3He-B is a quantum phenomenon. Only large flow perturbations are found to make the responses turbulent, such as the walls of a cubic container or the presence of invasive measuring probes inside the container.
Long-lived coherent spin precession of 3He-B at low temperatures around 0.2 Tc is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulat
ed experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.
A profound change occurs in the stability of quantized vortices in externally applied flow of superfluid 3He-B at temperatures ~ 0.6 Tc, owing to the rapidly decreasing damping in vortex motion with decreasing temperature. At low damping an evolving
vortex may become unstable and generate a new independent vortex loop. This single-vortex instability is the generic precursor to turbulence. We investigate the instability with non-invasive NMR measurements on a rotating cylindrical sample in the intermediate temperature regime (0.3 - 0.6) Tc. From comparisons with numerical calculations we interpret that the instability occurs at the container wall, when the vortex end moves along the wall in applied flow.
New techniques, both for generating and detecting turbulence in the helium superfluids 3He-B and 4He, have recently given insight in how turbulence is started, what the dissipation mechanisms are, and how turbulence decays when it appears as a transi
ent state or when externally applied turbulent pumping is switched off. Important simplifications are obtained by using 3He-B as working fluid, where the highly viscous normal component is practically always in a state of laminar flow, or by cooling 4He to low temperatures where the normal fraction becomes vanishingly small. We describe recent studies from the low temperature regime, where mutual friction becomes small or practically vanishes. This allows us to elucidate the mechanisms at work in quantum turbulence on approaching the zero temperature limit.
