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.     

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.     

Measurements on a Dynamic A-B Phase Boundary in Superfluid 3He at Very Low Temperatures

We present preliminary measurements of the dynamics of a moving A-B phase interface in superfluid ³ He at temperatures below 0.2T _c We initially stabilise the interface at low temperatures with a shaped magnetic field. We can then move the interface in a controlled manner by applying small additional time-dependent fields. The interface is created inside a quasiparticle radiator consisting of a cylindrical chamber in weak thermal contact with the refrigerant. Vibrating wire resonators inside the radiator allow us to monitor the temperature of the superfluid and to infer the heat generated by the interface motion. When we oscillate the interface at low frequencies, we measure spectacular oscillatory swings of the liquid temperature arising from the enormous change in the low lying density of states as the volume of the A-phase superfluid is alternately compressed and expanded. We have also observed hysteresis in the transition as a function of magnetic field. In particular, we observe a small history-dependent super-magnetisation of the B-phase prior to A-phase nucleation in the experimental chamber. When the system is in the metastable super-magnetised state we are able to observe a higher nucleation probability of the A-phase when the cryostat is exposed to neutrons.     

Non-linear Stationary Spin-waves in Superfluid 3He-B at Ultra-low Temperatures

We have performed detailed CW NMR measurements on superfluid ³ He-B in order to investigate stationary spin-wave modes in a texture well. Our results at high temperatures are consistent with previous work. However, we find that the spin dynamics is profoundly modified, even for small excitation amplitudes, for temperatures on the order of 200 K, substantially lower than the limit reached in previous investigations. We report the observation of non-linear spin-waves at ultra-low temperatures and their characterization in terms of a third-order anharmonic oscillator.     

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     

Vortex Dynamics in Superfluid 4He at Very Low Temperatures

Recently McClintock et al. observed the free decay of a vortex tangle in superfluid ⁴He at mK temperatures. Since the system at such low temperatures is free from normal fluid and usual mutual friction, the mechanism of the free decay is unknown. In order to understand this phenomenon, this work studies numerically the vortex dynamics without the mutual friction. The absence of mutual friction prevents the vortex from smoothing. The resulting kinked structure promotes vortex reconnection, thus making lots of small vortex loops. Such cascade process as breakup of vortices to smaller ones can decay the vortex line density. This paper describes the decay of vortex tangle under the localized induction approximation, and that of four vortex rings under the full nonlocal calculation.     

Kapton Capacitance Thermometry at Low Temperatures and in High Magnetic Fields

A sensitive Kapton foil capacitance sensor, with size of 9.5 mm×4.5 mm, has been developed and used as a thermometer at ultra-low temperatures down to 1.2 mK and in high magnetic fields. There is no visible magnetic field dependence up to 15 T. The sensor was calibrated with ³He melting pressure thermometer (MPT) and vibrating wire (VW) viscometer. With the silver powder sintered heat exchanger sandwich-like design, the thermal relaxation time is as short as a few minutes at the base temperature. The low temperature (below 1.2 K) reproducibility has been tested and is satisfied within experimental errors.     

Kelvin-Wave Cascades in Turbulent Superfluid 4He at Very Low Temperatures

There has been much interest recently in the mechanism by which superfluid (quantum) turbulence can decay in liquid ⁴He at very low temperatures, where mutual friction has a negligible effect. As in classical turbulence, energy must probably flow from larger to smaller length scales, and it has been suggested that on the smallest scales the relevant motion is a Kelvin wave on a quantized vortex with wave number greater than the inverse vortex spacing. By considering the behaviour of a simple model it is shown by computer simulations how energy can flow to shorter length scales (higher wave numbers) in a system of Kelvin waves, and how this process can lead to a remarkably simple Kelvin-wave energy spectrum. A discussion is included of the relevance of this model to the decay of superfluid grid turbulence at a very low temperature.     

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.     

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 Nucleation of Superfluid Turbulence at Very Low Temperatures by Flow Through a Grid

Recent experiments by Nichol et al. (cond-mat/0309245 v2) have been concerned with the dynamical behaviour of a grid oscillating in superfluid ⁴He at a very low temperature, where the normal fluid can be ignored. An interesting enhancement of the effective mass of the grid was observed above a first threshold velocity, without significant increase in damping. Only above a second larger threshold was there a large increase in damping, resulting, we presume, from the generation of turbulence. We show now how the increase in effective mass can be understood in terms of an adiabatic response of the remanent quantized vortices that are knoum to be present, usually, in superfluid helium. Only at the larger threshold is the adiabatic response replaced by a dissipative evolution into a turbulent tangle of vortex lines. We present a semi-quantitative analysis of the experimental results, which suggests strongly that the remanent vortices must take the form of a rather high density of vortex loops attached to the grid. But confirmation of our ideas must await the completion of further experiments and a programme of non-trivial computer simulations.     

NMR Spectroscopy of Adsorbed 129Xe at Low Temperatures and High Magnetic Fields

In this paper we report measurements of the nuclear magnetic resonance (NMR) spectrum of ¹²⁹Xe adsorbed on silica gel and Grafoil^? substrates in a 15 tesla magnetic field and temperatures in the range 10 mK to 1 K. Liquid ³He is used to shorten the spin lattice relaxation time of the ¹²⁹Xe spins and obtain a high degree of spin polarization of over 40% in around a day. The ¹²⁹Xe NMR spectrum generally exhibits two lines. We show that one line corresponds to the monolayer of surface xenon atoms and the other line to the monolayers of bulk solid xenon between the substrate and the surface monolayer. By comparing the spectra and relaxation rates for xenon of different ¹²⁹Xe concentrations and by adding ⁴He we were able to investigate the ¹²⁹Xe interlayer coupling. The work has important implications in the study of porous materials using hyperpolarized gases, the study of surface atoms by NMR and the production of hyperpolarized species by the brute force technique.     

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.     

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     

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.     

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.     

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.     

Thermal Conductivity of Superconductor Sr2RuO4 at Low Temperatures and Magnetic Fields

The temperature dependence of thermal conductivity of Sr₂RuO₄ is investigated by the Boltzmann equation approach. We consider both the isotropic and anisotropic gap energy in superconducting state in the absence and presence of low magnetic field, and obtain the temperature dependence of the components of thermal conductivity in both cases. In the case of isotropic gap, it is proportional to T ^1/2, whereas in the case of anisotropic gap, K _xx ∝T ^?1,K _yy ∝T, and K _xy =K _yx =constant. Furthermore, we show that at a low magnetic field K behaves as in the case of the zero magnetic field.