The Damping of a Quartz Tuning Fork in Superfluid 3He-B at Low Temperatures

We have measured the damping on a quartz tuning fork in the B-phase of superfluid ³He at low temperatures, below 0.3T _c. We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid ³He-B and in superfluid ⁴He at low temperatures. In superfluid ⁴He the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid ³He the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid ³He-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid ⁴He.     

Coherent Spin Precession in Superfluid 3He-B Excited in a Field Minimum at Low Temperatures

No Heading The persistent precessing domain (PPD) is an isolated region of coherent spin precession which is observed in the B phase of superfluid ³He at the lowest achievable temperatures. It has many unusual properties and its free decay can exceed 1000s at the lowest temperatures. Previous observations of the PPD were highly irreproducible but we now find the PPD to be very reproducible when there is a field minimum along the cell axis. Here we discuss measurements of the PPD as we control the magnetic field profile, allowing the depth of the minimum to be adjusted.PACS numbers: 67.57.Lm, 67.57.Jj, 67.57.Fg     

The Thermal Damping of an Aerogel Resonator in Superfluid 3He-B at Ultra Low Temperatures

No Heading We present measurements of the thermal damping of a cylindrical aerogel sample oscillating in superfluid. ³He-B in the low temperature regime. The measurements are made at low pressures where the ³He confined in the aerogel is normal. As in the case of conventional vibrating wire resonators, the thermal damping arises from quasiparticle collisions at the wire surface and is enhanced by many orders of magnitude by Andreev scattering from the superfluid backflow around the resonator. However, in the case of aerogel, incoming quasiparticles must be absorbed and thermalised within the aerogel before being re-emilled.PACS numbers: 67.57.Bc, 67.57.De, 67.57.Hi, 67.57.Pq.     

Non-linear Spin Waves on Topological Defects of Texture in Superfluid 3He-B

We have observed non-linear behaviour of stationary spin waves localised on textural topological defects. We can explain our results in the framework of the Schrödinger equation with feedback. The new method gives us the ability to see many topological defects, which are undistinguished by traditional methods of NMR. We have found that some of the non-linear spin wave modes can be responsible for the extremely long lived induction decay signals called Persistent signals.     

The Dynamic Texture of Superfluid 3He-B at Very Low Temperatures and in High Magnetic Fields

No Heading We report experiments using a pair of crossed vibrating wire resonators (VWRs) in the B phase of superfluid ³He in the zero temperature ballistic limit and in magnetic fields up to the B to A phase transition field of 340 mT. The VWRs are sensitive mechanical probes of energy gaps, textures and turbulent flow. In high magnetic fields the energy gap is no longer isotropic but significantly distorted, and the damping measured by the VWRs increases. With the crossed pair, we find that we can reduce the damping measured by one VWR when we increase the drive on the other one. We suggest that the reduction arises from the orientation of the surrounding texture by superflow and the screening of quasiparticles by the creation of superfluid turbulence.PACS numbers: 67.57.Fg, 67.57.Hi.     

Domain Walls in Superfluid 3He-B

No Heading We consider domain walls between regions of superfluid ³He-B in which one component of the order parameter has the opposite sign in the two regions far from one another. We report calculations of the order parameter profile and the free energy for two types of domain wall, and discuss how these structures are relevant to superfluid ³He confined between two surfaces.PACS numbers: 67.57.Np     

Hydrostatic Theory of Superfluid 3He-B

The determination of the texture of the order parameter is important for understanding many experiments in superfluid ³He. In addition to reviewing the theory of textures in superfluid ³He-B we give several new results, in particular on the surface parameters in the Ginzburg–Landau region and bulk parameters at arbitrary temperature. Special attention is paid to separate the results that are valid at all temperatures from those which are limited to the Ginzburg–Landau region. We study the validity of a trivial strong-coupling model, where the energy gap of the weak-coupling theory is scaled by a temperature dependent factor. We compare the theory with several experiments. For some quantities the theory seems to work fine and we extract the dipole–dipole interaction parameter from the measurements.     

Dynamic Remanent Vortices in Superfluid 3He-B

We investigate the decay of vortices in a rotating cylindrical sample of ³He-B, after rotation has been stopped. With decreasing temperature vortex annihilation slows down as the damping in vortex motion, the mutual friction dissipation α(T), decreases almost exponentially. Remanent vortices then survive for increasingly long periods, while they move towards annihilation in zero applied flow. After a waiting period Δt at zero flow, rotation is reapplied and the remnants evolve to rectilinear vortices. By counting these lines, we measure at temperatures above the transition to turbulence ∼0.6 T _c the number of remnants as a function of α(T) and Δt. At temperatures below the transition to turbulence T≲0.55 T _c, remnants expanding in applied flow become unstable and generate in a turbulent burst the equilibrium number of vortices. Here we measure the onset temperature T _on of turbulence as a function of Δt, applied flow velocity v=v _n−v _s, and length of sample L.     

Measurement of Turbulence in Superfluid 3He-B

The experimental investigation of superfluid turbulence in ³He-B is generally not possible with the techniques which have been developed for ⁴He-II. We describe a new method by which a transient burst of turbulent vortex expansion can be generated in ³He-B. It is based on the injection of a few vortex loops into rotating vortex-free flow. The time-dependent evolution of the quantized vorticity is then monitored with NMR spectroscopy. Using these techniques the transition between regular (i.e. vortex number conserving) and turbulent vortex dynamics can be recorded at T ～ 0.6 T_c and a number of other characteristics of turbulence can be followed down to a temperature of T ? 0.4 T_c. PACS numbers: 47.37, 67.40, 67.57.     

High Frequency Sound in Superfluid 3He-B

We present measurements of the absolute phase velocity of transverse and longitudinal sound in superfluid ³He-B at low temperature, extending from the imaginary squashing mode to near pair-breaking. Changes in the transverse phase velocity near pair-breaking have been explained in terms of an order parameter collective mode that arises from f-wave pairing interactions, the so-called J=4^? mode. Using these measurements, we establish lower bounds on the energy gap in the B-phase. Measurement of attenuation of longitudinal sound at low temperature and energies far above the pair-breaking threshold, are in agreement with the lower bounds set on pair-breaking. Finally, we discuss our estimations for the strength of the f-wave pairing interactions and the Fermi liquid parameter, F ₄ ^s .     

The Decay of Turbulence in Superfluid 3He-B

A brief summary of our understanding of homogeneous turbulence in a classical fluid and in superfluid ⁴ He is followed by our first thoughts on the extension of the relevant theoretical ideas to turbulence in superfluid ³ He-B, taking as a model of this system a hypothetical BCS superfluid with s-state pairing and parameters appropriate to the real system. Important and fundamental differences can be expected between superfluid turbulence in the two isotopes, which could be explored with appropriate experiments.     

Dissipative Currents in Superfluid 3He-B Weak Links

Recent measurements of dissipative currents in pressure-biased weak links of superfluid ³He-B are discussed. It is pointed out that the theoretical understanding of their resugts is unsatisfactory. As one candidate model to explain them, we consider the process of mugtiple Andreev reflections (MAR). Connection of MAR to bound quasiparticle states inside ballistic contacts is discussed. As an explicit example we analyze the current in a short pressurebiased ballistic ³He-B constriction. It is shown that the dissipative part of the current does not depend on the spin-orbit rotation matrices.     

Vortex Formation in Neutron-Irradiated Rotating Superfluid 3He-B

A convenient method to create vortices in meta-stable vortex-free superflow of ³He-B is to irradiate with thermal neutrons. The vortices are then formed in a rapid non-equilibrium process with distinctive characteristics. Two competing explanations have been worked out about this process. One is the Kibble-Zurek mechanism of defect formation in a quench-cooled second order phase transition. The second builds on the instability of the moving front between superfluid and normal ³He, which is created by the heating from the neutron absorption event. The most detailed measurements with single-vortex resolution have been performed at temperatures close to T_c. In the first half of this report we summarize the two models and then show that the experimentally observed vortices originate from the Kibble-Zurek mechanism. In the second half we present new results from low temperatures. They also weakly support the Kibble-Zurek origin, but in addition display superfluid turbulence as a new phenomenon. Below 0.6 T_c the damping of vortex motion from the normal component is reduced sufficiently so that turbulent vortex dynamics become possible. Here a single absorbed neutron may transfer the sample from the meta-stable vertex-free to the equilibrium vortex state. The probability of a neutron to initiate a turbulent transition grows with increasing superflow velocity and decreasing temperature. PACS numbers: 47.32, 67.40, 67.57, 98.80.     

Boundary Conditions at the Bulk–Aerogel Interface of Superfluid 3He-B

We study the interface between bulk and aerogel impregnated with ³ He-B. The magnetic susceptibility at the interface determines a boundary condition for the texture, which can be parameterized by the orbital vector L. We use Ginzburg–Landau theory to calculate the boundary condition assuming homogeneous aerogel and a sharp interface. Recent NMR measurements give reason to conjecture that L tends to be parallel to interface. Our numerical calculations confirm this conjecture in the Ginzburg–Landau (GL) regime. However, the orienting energy is one order of magnitude smaller than at a solid wall, and therefore can easily be overshadowed by a nearby wall.     

Experiments on the Twisted Vortex State in Superfluid 3He-B

We have performed measurements and numerical simulations on a bundle of vortex lines which is expanding along a rotating column of initially vortex-free ³He-B. Expanding vortices form a propagating front: Within the front the superfluid is involved in rotation and behind the front the twisted vortex state forms, which eventually relaxes to the equilibrium vortex state. We have measured the magnitude of the twist and its relaxation rate as function of temperature above 0.3T _c. We also demonstrate that the integrity of the propagating vortex front results from axial superfluid flow, induced by the twist.      

Orbital Viscosity in Superfluid 3He-B in a Magnetic Field

No Heading Orbital viscosity is usually associated with the A phase of superfluid ³He which has a finite orbital angular momentum even in zero magnetic field. The B phase has no orbital angular momentum in zero magnetic field, but both spin and orbital angular momenta are induced by a field. The Leggett equations for spin dynamics assume that the orbital angular momentum can only charge on timescales much longer than those involved in spin dynamics. We calculate the orbital viscosity of the B phase in both the hydrodynamic and ballistic limits. At low temperatures the orbital viscosity becomes vanishingly small which gives rise to the possibility of coupled spin-orbit dynamics.PACS numbers: 67.57.Hi, 67.57.Lm     

New Modes of Stable Spin Precession in Superfluid 3He-B

The cw NMR response of ³ He-B is investigated in large rf excitation fields, which exceed in magnitude the equivalent of the spin-orbit coupling. New states of stable spin precession are observed. The Leggett-Takagi spin-dynamic equations are solved numerically with the proper experimental parameters, the results are found to reproduce most of the experimental features, and allow an identification of the new modes. Vortex lines or vortex-free counterflow in the rotating superfluid have not been found to influence the measured NMR signatures of the new modes.     

Superfluid 3He-B Vortex Simulations inside a Rotating Cylinder

No Heading We study numerically vortex dynamics in superfluid ³He-B by solving the full Biot-Savart equations inside a rotating cylinder. The initial vortex configuration seems to have an essential role whether the growth process starts or not. The growth process is, at least at the early stages of simulations, mostly governed by the reconnections with cylinder boundary. In order to see a large increase in vortex density one should go below 0.5T_c in temperature, somewhat lower than what is observed in the experiments.PACS numbers: 47.32, 67.57.     

Vortex Rings in Superfluid 3He–B at Low Temperatures

Turbulence in classical fluids has far-reaching technological implications but is poorly understood. A better understanding might be gained from studying turbulence in quantum systems. In a pure superfluid (at low temperatures), there is no viscosity and vortex lines are quantised. Quantum turbulence consists of a tangle of quantised vortex lines which interact via their self-induced flow. We have recently developed techniques for detecting vortices in superfluid ³He–B in the low temperature limit. We find that the transition to turbulence from a moving grid occurs by the entanglement of emitted vortex rings. Here, we discuss the propagation of the ballistic vortex rings emitted at low grid velocities. We have measured the temperature at which the rings decay before reaching the detectors. Our results, at two different pressures, confirm that the vortex rings decay in accordance with mutual friction.     

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in superfluid ³ He at ultralow temperatures. The aerogel dik is attached to a goal post shaped vibrating wire resonator and immersed in liquid ³ He cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below <0.11T_c. At higher pressures we observe large temperature dependent frequency shifts, reminiscent of torsional oscillator experiments. We find the transition temperature at 5 bar to be around 600K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of ³ He in aerogel in the ultralow temperature regime.