The Response of a Mechanical Oscillator at the Superfluid 3He AB Interface

From our long experience of using profiled magnetic fields to stabilize and manipulate the AB phase boundary in superfluid ³He in the zero-temperature limit, we have constructed a cell where we can place the AB interface in the vicinity of a pair of crossed vibrating wire resonators (VWRs). The VWRs provide sensitive mechanical probes of the A and B phase energy gaps and textures. Here we present preliminary resugts where we observe the dynamic response of the VWR at the AB interface.     

Effect of Strong Magnetic Fields on Superfluid 3He in 98% Porosity Aerogel

No Heading We report our results of shear acoustic impedance measurements performed on superfluid ³He in 98% porosity silica aerogel. Experiments in high porosity aerogel provide unique opportunity to study the influence of disorder on a p-wave superfluid and compare the behavior with that of the well understood pure bulk. Our experiment is designed to detect acoustic signatures from both bulk liquid and liquid in aerogel. In the past, experiments on ³He in aerogel have been conducted in zero or low magnetic fields (< 1 tesla). We made measurements in magnetic fields as high as 15 tesla at 28.4 and 33.5 bars and observed a new phase in aerogel induced by magnetic fields splitting the superfluid transition into two.PACS numbers: 67.57Pq, 67.80Mg     

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.     

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 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     

Theory of Acoustic Impedance of Superfluid 3He

No Heading A microscopic theory of transverse acoustic impedance of superfluid ³He at low temperatures is presented. we calculate the stress tensor of superfluid ³He as a response to the oscillating rough wall. For that purpose, we extend a quasi-classical theory based on the random S-matrix model to time dependent problems. We show that by virtue of the pair breaking mechanism the transverse impedance can be finite even at T=0 K. This is in contrast to the theories using the quasi-particle distribution function which predict that the impedance tends to zero like a Yosida function.PACS numbers: 67.57.Np, 67.57.Jj     

Superfluid Phases of 3He in Aerogel

No Heading Formal derivation of criterion for selection of superfluid phases of ³He in aerogel is presented. At the strength of the derived criterion variation of the order parameter of B-like phase in magnetic field differs from that of B-phase of pure ³He. Possible observable consequence of this difference is discussed.PACS numbers: 67.57.Pq, 67.57.Bc, 67.57.De     

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     

Phase transitions in the growth of4He films

Using a microscopic, variational approach we examine the growth of⁴He absorbed to graphite and alkali substrates. We find that superfluid layers are formed and their behavior as a function of coverage is closely related to the one of a purely two-dimensional superfluid. The growth of a new layer undergoes a phase transition from a cluster formation into the connected superfluid when the coverage is increased. Based on the important connection to the two-dimensional fluid we propose a microscopic theory of quantum vortices in⁴He films at zero temperature, in which single vortices are treated as quasiparticles. We calculate the energy needed to create the single vortex, vortex inertial mass, microscopic interaction between vortices and binding energy of the vortex-antivortex pair as a function of density. We predict that at the⁴He superfluid density less than about 0.037 Å^–2 the binding energy of the pair becomes negative, indicating a phase transition into a new state where vortex-antivortex pairs are spontaneously created.     

SH-SAW Sensor for Superfluid 3He

No Heading We have developed a new technique to study the transverse acoustic properties of superfluid ³He, employing a shear horizontal surface acoustic wave (SH-SAW) sensor. The transverse acoustic impedance can be obtained from the velocity and damping of SH-SAW which acoustically couples with liquid ³He all the interface. Since ultrasonic measurements provide the information about superfluid order-parameter through the excitation of collective modes, the SH-SAW sensor is expected to be a useful tool to study the boundary effect of superfluid ³He. Preliminary measurements were carried out at pressures of 17 and 23 bar, by the pulse transmission method at a frequency of 70 MHz. At 17 bar, imaginary squashing mode was observed as the sharp drop of the imaginary part of acoustic impedance. At 23 bar, the supercooled A-B phase transition was observed, as a jump of the real part of acoustic impedance, which was not observed in the warming process.PACS numbers: 67.57.Jj, 43.58.+z     

Spin Relaxation in 3He-A1 Measured by Magnetic Fountain Pressure

No Heading Measurements of spin relaxation in superfluid ³He-A₁ phase as inferred from the decay of magnetic fountain pressure are reported in magnetic fields up to 8 testa and in pressure between 1 and 29 bars. Unlike in the previous experiment¹, the magnetic fountain pressure detector is placed in an apparatus containing A₁ phase liquid and there is no interface with any other phases of ³He. An abrupt large change in relaxation time observed in the previous experiment is now absent near the middle of A₁ phase. This observation supports the idea that the origin of the abrupt change in relaxation time is the presence of A₁/A₂ interface.PACS numbers: 67.57.–z, 67.65.+z, 72.25.–b     

The Equilibrium A-B Transition in Low Density Aerogels

No Heading We have measured in detail the NMR spectra of superfluid ³ He inside two different silica aerogels, one with a porosity of 99.3% and the other 98.6%. From these spectra, we are able to determine the equilibrium A-B transition temperatures in both aerogel samples as a function of hydrostatic pressure. We find that the slope of the reduced A-B transition temperature, 1- T_AB/T_c, vs. pressure is only about one third that seen for the bulk A-B transition, despite the fact the T_c for the two samples is suppressed very modestly, by only 4% and 8% at 34 bars. We argue from this that the presence of the aerogel stabilizes an equal-spin pairing which is district from that stable in the bulk.PACS numbers: 67.57 Pq, 67.57 Lm     

Thermal phenomena in the flow of superfluid 3He through a weak link

No Heading We report on experiments performed with a weak link which was the only flow connection between two volumes of ³He. The deflection of a flexible wall between the volumes was measured to monitor the flow through the weak link as well as to measure the pressure difference across it. The temperature of the main volume was changed in steps of approximately 0.2 mK. After these temperature steps a fountain pressure developed and decayed on a time scale of several hundred seconds. This thermomechanical effect was found in normal and in superfluid ³He. We did not observe any influence of the quantum phase difference on the heat conductivity.PACS numbers: 67.57.De, 67.57.Fg, 74.50.+r, 85.25.Cp     

Phase diagram of turbulence in superfluid 3He-B

No Heading In superfluid ³He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52–0.59 T_c and has a narrow width of 0.06 T_c while at zero pressure turbulence is not observed above 0.45 T_c.PACS numbers: 47.37, 67.40, 67.57     

Phase Slips and Josephson Weak Links in Superfluid Helium

When superfluid ⁴He flows through a submicron aperture, the velocity is limited by a critical value which marks the onset of quantized vortex creation. The evolution of the vortices causes the quantum phase across the aperture to change by 2π, leading to a detectable drop in flow energy. Recent studies of these phase slip events have provided new insights into the nucleation mechanisms for quantum vortices. By contrast, superfluid ³He passing through a submicron aperture exhibits nonlinear hydrodynamics, characterized by a Josephson-like current phase relation. Recent experiments have revealed a multitude of effects analogous to phenomena observed in superconductors. The experiments also reveal unexpected effects such as bistability, π-states, and novel dissipation mechanisms. PACS numbers: 67.57.-z, 74.50.+r, 67.40.Hf, 67.40. Vs.     

Impurity Scattering Effect on Superfluid Phases of 3He in 97.5% Porous Silica Aerogel

No Heading NMR studies of superfluid ³He in 97.5% aerogel have been performed in a magnetic field of 28.4 mT. A small-angle neutron scattering experiment on the structure of the aerogel shows that the average separation distance of silica strands is 54 nm. The aerogel strands were covered with a few layers of solid ³He whose magnetization shows Curie-Weiss behaviour. On cooling process A-like phase appeared at suppressed superfluid transition temperature T_C^aero and B-like phase appeared at lower temperatures although only the B-like phase was observed up to T_C^aero on warming process above 2.1 MPa. The superfluid transitions in aerogel always occur below the AB phase transition temperature of bulk liquid at all pressures. An isotropic inhomogeneous scattering model(IISM) proposed by Thuneberg et al. explained well the observed suppressed T_C^aero in 97.5% with the radius 59 nm of voids in this model. This radius is similar with the average strand separation distance of 54 nm measured in the structural analysis. This similarity of two lengths shows the connection of the suppression of T_C^aero with the actual average separation distance of the silica strands.PACS numbers: 67.57.Pq, 67.80.Jd     

Textural Effects and Spin-Wave Radiation in Superfluid 3He Weak Links

The Josephson coupling between two volumes of superfluid ³He-B also couples the phase difference to the spin-orbit texture of the order parameter. As a result, the equilibrium configuration of the macroscopic texture depends on the phase difference. If the junction is biased by a pressure head, the Josephson oscillations of the supercurrent are accompanied by an oscillation of the texture close to the junction. This leads to a radiation of spin waves from the weak link, and thus contributes to the dissipative dc currents flowing through it. PACS numbers: 67.57.De, 67.57.Fg, 67.57.Np.     

Non-linear Mechanical Response of the A-like Phase of Superfluid 3He in Aerogel

We present measurements of the response of the A-like phase of superfluid ³He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid ³He at low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.     

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.