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.     

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.     

Spatial Manipulation of the Persistent Precessing Spin Domain in Superfluid 3He-B

Using pulsed NMR we have been studying the properties of the persistent precessing domain (PPD) in superfluid ³He-B at ugtralow temperatures. These precessiog spin domains are very long-lived, persisting for periods of over half an hour under favourable conditions. In the current experiment, by using two NMR coils, we are able to monitor the spatial location of the domain. The PPD is trapped in a field minimum along the axis of the cell, the position of which we can manipulate by variation of the field gradient. We find that the signal lifetime becomes much shorter and independent of temperature when the region of precession is brought into close proximity to the closed end of the experimental cell, suggesting that an extra temperature-independent dissipation mechanism comes into play in the vicinity of the cell walls.     

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.      

Torsional Oscillations of a Rotating Column of 3He-B

No Heading We have analysed the axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid. We have investigated how changing the temperature affects the growth rate of the disturbances. We find that, in the long axial wavelength limit the condition q = /(1 – ) = 1, where and are temperature-dependent mutual friction parameters, is the crossover between damped and propagating Kelvin waves. Thus at temperatures for which q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. These results are in agreement with the recent discovery of Finne et al¹ of an intrinsic condition for the onset of quantum turbulence in ³He-B.PACS numbers: 67.40. Vs, 67.57.–z     

The Onset of Vortex Production by a Vibrating Wire in Superfluid 3He-B

We present measurements of the force-velocity response of a vibrating wire resonator in superfluid ³He-B at very low temperatures. At low velocities the response is dominated by intrinsic (vacuum) damping whilst at high velocities it is dominated by pair-breaking. At intermediate velocities there is a series of small plateaus where the velocity often shows small oscillations. We believe that the behaviour results from the stretching of vortices pinned to the wire. The vortices grow and self-reconnect, emitting a vortex ring. The behaviour is very sensitive to the presence of surrounding vortices generated by a neighbouring vibrating wire.     

On the Local Stability of the Quadrupole Vortex in Superfluid 3He-B

Studies with a constrained Ginzburg–Landau approach have suggested that the Quadrupole core vortex in³He-B should be a saddle point of the free energy (G. E. Volovik and M. M. Salomaa, JETP Lett.45, 56 (1987)). We have carried out a careful numerical analysis in the framework of the quasiclassical theory with the conclusion that the core in fact is a local minimum. No constrains were imposed on the phase space. The Quadrupole vortex can be a contender for the second vortex in the Manchester group experiment (Bevan et al., JLTP (1987)).     

Time-of-Flight Measurements on Quantized Vortex Lines in Rotating 3He-B

Vortex loops are injected into a long cylindrical sample of rotating vortex-free superfluid ³He-B. Using non-invasive NMR techniques, we measure the time required for them to expand along the sample axis to form rectilinear vortex lines. From the axial flight time we deduce the dissipative mutual friction parameter a which is found to agree with previously reported measurements. The flight time displays no anomaly at 0.6T _c, where the character of the vortex dynamics abruptly changes from regular over-damped flow to turbulence.     

Anomalous Damping of a Low Frequency Vibrating Wire in Superfluid 3He-B due to Vortex Shielding

We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid ³He at zero pressure and at temperatures below 200 μK. The vibrating wire has a low resonant frequency of around 60 Hz. At low velocities the motion of the wire is impeded by its intrinsic (vacuum) damping and by the scattering of thermal quasiparticle excitations. At higher velocities we would normally expect the motion to be further damped by the creation of quasiparticles from pair-breaking. However, for a range of temperatures, as we increase the driving force we observe a sudden decrease in the damping of the wire. This results from a reduction in the thermal damping arising from the presence of quantum vortex lines generated by the wire. These vortex lines Andreev-reflect low energy excitations and thus partially shield the wire from incident thermal quasiparticles.     

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.     

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 .     

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.     

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.     

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     

Coherent Bragg Scattering of Light by a Vortex Lattice in Rotating Superfluid He

Proposed observation of coherent Bragg scattering by a lattice of vortices in uniformly rotating superfulid Helium is examined. We present the calculations of the cross section for different parameter values, as well as simulations of the detected intensity of the Bragg peaks for triangular arrays with varied degrees of distortion. Within this frame, a potentially feasible experiment is outlined to provide direct evidence of vortices with an atomic-scale core in superfluid Helium.     

Inertial and Fluctuational Effects on the Motion of a Bose Superfluid Vortex

We study the motion of a vortex under the influence of a harmonic force in an approximately two dimensional trapped Bose-condensed gas. The Hall-Vinen-Iordanskii equations, modified to include a fluctuational force and an inertial mass term, are solved for the vortex motion. The mass of the vortex has a strong influence on the time it takes the vortex to escape the trap. Since the vortex mass also depends on the trap size we have an additional dependence on the trap size in the escape time which we compare to the massless case.     

Persistent Precessing Texture-Trapped Domains in Low Temperature Superfluid 3He

It has recently been discovered that at temperatures below about 0.2T _C in superfluid ³ He-B, pulsed NMR excitation can generate a new coherently precessing spin state which can have a lifetime of tens of seconds. The free induction decay signal from this state has been called the persistent induction signal (PIS). The earlier observations of the PIS have found it to be highly irreproducible indicating a strong connection with the magnetic texture. Here we describe measurements of the PIS within an experimental cell which was designed to fix the textural configuration of the superfluid. The resulting PIS signals are now far more reproducible allowing a more systematic study of the behaviour which we present here. Furthermore in the latest cell the decay of this signal has been observed to last for up to 4 minutes at the lowest temperatures. While the precessing state is readily accessible to observation, at these temperatures it is a very delicate object and we can immediately see the influence of background radiation on the time evolution of the decay.