Dissipation in Superfluid 3He Weak Links

We suggest a new interpretation of the Berkeley data on the dissipation of superflow in Josephson junctions in superfluid ³He-B. The measurements are well described by the following relation between the current through a junction and the pressure head applied to it (current-pressure relation or CPR): $I = G_1 P + G_2 \sqrt P $ . The Berkeley group has proposed an explanation based on 1) ballistic removal of quasiparticles from the junction; 2) dissipative motion of the anisotropy axis of the order parameter inside the junction. We argue that part 1) of the model, which is responsible for the G ₂ part of the CPR, is invalid, since it presumes the existence, in the bulk, of quasiparticles with energies inside the superfluid gap. Part 2) which is responsible for the G ₁ term implies that the anisotropy axis of the order parameter strongly depends on the phase difference across the junction. Our agternative model is based on mechanisms well known in superconductors: dissipation due to time lag of inequilibrium order parameter and/or Andreev reflection of quasiparticles trapped inside the junction. For the parameters of the Berkeley experiment these models give the same order of magnitude for the G ₁ in the CPR, and are in rough agreement with the experiment. The nature of the G ₂ term remains mysterious. It could arise due to saturation of the current of Andreev-scattered quasiparticles if the quasiparticle relaxation time in the junction is considerably longer than in normal Fermi liquid.     

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.     

Search for New Materials and Techniques for Superfluid Weak Links

Superfluid ³ He-flow in channels essentially smaller than the coherence length would be challenging. In this paper, a technique is described which allows the production of almost circularly shaped 10 nm diameter holes in nitrocellulose films of 14 nm thickness. These geometrical dimensions also allow Josephson effect experiments in superfluid ⁴ He of about 1% superfluid density around temperatures of 0.9999 T. The hole density in the membranes can be as high as 10 ⁸ cm^–2 which allows one to work with high Josephson currents while at the same time the decoherence effect of vibrations is minimised. Alternative solutions for even smaller holes in several differently designed membranes are discussed.     

Polarization Effects in Superfluid 4He

A theory of thermoelectric phenomena in superfluid ⁴He is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid ⁴He generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.     

Superfluid3He in restricted geometries

It is shown that finite size effects stabilize a variety of phases in superfluid³He which do not occur in the bulk liquid. These phases are formed at temperatures at which the coherence length is comparable with the smallest linear dimension of the system. Right circular cylindrical geometries are considered explicitly.     

Induced Gravity in Superfluid 3He

The gapless fermionic excitations in superfluid ³ He-A have the relativistic spectrum close to the gap nodes. This allowed us to model the modern cos-mological scenaria of baryogenesis and magnetogenesis. The same massless fermions induce another low-energy property of the quantum vacuum – the gravitation. The effective metric of the space, in which the free quasiparticles move along geodesies, is not generally flat. Different order parameter textures correspond to curved effective space and produce many different exotic metrics, which are theoretically discussed in quantum gravity and cosmology. This includes the condensed matter analog of the black hole and event horizon, which can be realized in the moving soliton. This will allow us to simulate and thus experimentally investigate such quantum phenomena as the Hawking radiation from the horizon, the Bekenstein entropy of the black hole, and the structure of the quantum vacuum behind the horizon. One can also simulate the conical singularities produced by cosmic strings and monopoles; inflation; temperature dependence of the cosmological and Newton constants, etc.     

Rotating Superfluid 3He in Aerogel

Rotational effects on textures of superfluid ³He in aerogel with 98% porosity at a pressure 3.0 MPa were investigated by cw-NMR measurement at 700 kHz (H ₀=22 mT) under rotation up to 2π rad/s. At rest, the superfluidtransition to the A phase occurred at T ^aerogel _c =2.07 mK and the A phase was supercooled down to T ^aerogel _A→B==1.73～1.80 mK and became the B phase in the cooling process. In the warming process, the B phase was superheated up to T ^aerogel _c . In the B phase, a new peak appeared in the NMR spectrum by rotating the sample. The intensity of this peak increased as the rotation speed increased almost linealy to Ω and started to be saturated for Ω≥Ω _c. We attributed the new peak to the textural change caused by the counter flow and the onset of the saturation at Ω _c to the onset of vortex nucleation in aerogel. On deceleration, the peak intensity decreased and disappeared at Ω=Ω _v. Further decreasing Ω, the peak intensity increased even at Ω=0. The counterflow peak observed at Ω=0 indicates the existence of persistent current induced by pinned vortices in aerogel. In the A phase, we did not find any noticeable change in the NMR spectrum under the rotation speed up to 2π rad/s, or by cooling through T _c with or without rotation. We concluded that the ${\hat \ell }$ texture in the A phase was strongly pinned to aerogel. No spin wave satellite signal localized at a soft, core vortex was observed in contrast to the bulk A phase.     

Counterflow-Driven Textural Phase Transitions in Superfluid 3He-A1

We have studied second sound propagation through superftuid ³ He-A ₁ filling a rectangular resonator equipped with 3 pairs of transducers. The -texture was manipulated using one transducer to drive an oscillatory counterflow while measuring the resonant response of an orthogonal transducer pair. We observed abrupt signal changes and hysteresis effects depending on drive frequencies and amplitudes. We analyzed our experiments by examining planar -textures strongly coupled to the linear second sound wave equation. Evidence of first-order phase transitions was obtained numerically. The results are qualitatively consistent with the experimental findings. Our physical intuition did not anticipate these striking discontinuous phenomena.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

Vortex-Loops and Phase Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴ He and ³ He. A fast solidification event in the superfluid results in a local release of pressure and a velocity field in the superfluid. This in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with experiments on heterogeneous nucleation.     

Superfluid 3He in the Zero-Temperature Limit

Superfluid ³He has a hierarchy of properties, each manifest as a ‘superfluid’. There is the mass superfluid, the spin superfluid and there should also be an orbital superfluid. These three ‘super’ fluids respond differently to the interpenetrating normal fluid and demand different temperature ranges to be studied fully. We discuss here the importance of work at very low temperatures, how we can cool to the lowest temperatures and finally present a selection of low temperature experiments which illustrate aspects of multiphase nature of the superfluid and of the three ‘superfluids’ mentioned above. PACS numbers: 05.70 Ln, 05.70 Jk, 64.     

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     

Vibrating Wire Thermometry in Superfluid 3He

We report systematic measurements of the response of a Vibrating Wire Resonator (VWR) in normal and superfluid liquid ³He. Special attention has been paid to the hydrodynamic regime of the superfluid B-phase, where the response parameters of the VWR do not follow a simple law. We show that a simple interpolation between the region where first order slip-corrections can be applied and the ballistic regime is insufficient. Measuring an empirical effective viscosity, we propose a temperature calibration method which allows the use of VWRs as a secondary thermometer at intermediate and high pressures in the temperature range 0.2 T _c < T < 50 mK.     

Vortex Mutual Friction in Superfluid 3He

We give a full account of our extensive measurements of vortex mutual friction in rotating superfluid ³He, in both the A- and B-phases. The B-phase results are in qualitative agreement with a theory based on the concept of “spectral flow”; the agreement becomes quantitative if an effective energy gap of 0.63 Δ is used, but the Justification for such a substitution is not clear. The vortex core transition, at first not seen because of metastability and hysteresis, has now been observed. Detailed investigation suggests that the high temperature vortex state is a temperature dependent mixture of at least two vortex types. The A-phase mutual friction is found to be well described by two hydrodynamic coefficients, the orbital viscosity and the orbital inertia. The latter corresponds to an orbital angular momentum per Cooper pair of (0.0015 ± 0.0017 ) ħ, consistent with the prediction of the spectral flow theory. We find that the most uniform l texture is obtained by cooling through T_c while rotating, and then stopping rotation. Detailed investigation of textural memory effects shows that the uniform l-up and l-down textures are associated with opposite directions of rotation. We discuss the various types of texture that may be formed in our experiments. Finally, we compare our mutual friction results with those found in ⁴HeII.     

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     

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature T _c ^a is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/T _c ^a ) at 0.9T _c ^a as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.     

Sound Modes of Superfluid 3He in Aerogel

We present the results of experiments on sound propagation at audio frequencies in ³ He-filled aerogel. Sound modes were observed at temperatures of 0.8–100 mK in an aerogel sample of 98% porosity. We find that below T _c for superfluid ³ He in the aerogel matrix the speed of sound in the composite system increases by as much as 1.5%. Also below the aerogel T _c new modes appear which correspond to propagation speeds of up to 10 m/s.     

Zeeman Splitting and Nonlinear Field-Dependence in Superfluid 3He

We have studied the acoustic Faraday effect in superfluid ³He up to significantly larger magnetic fields than in previous experiments achieving rotations of the polarization of transverse sound as large as 1710°. We report nonlinear field effects, and use the linear results to determine the Zeeman splitting of the imaginary squashing mode (ISQ) frequency in ³He-B.     

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of ³He in different samples of silica aerogel. Several of these samples have been characterized using x-ray imaging, yielding information about the microstructure of the aerogel. In comparing new measurements on a 99.5% sample with previous observations on the behavior of ³He in 98% porous aerogel we have found evidence for a scaling of the superfluid transition temperature to the correlation length of the aerogel. Furthermore, the superfluid density exhibits a similar universal behaviour over a range of values of reduced temperature. We discuss these new results in the context of superfluid pairing in the presence of a correlated disorder, specifically focussing on the fractal nature of the aerogel.     

Thermodynamic Magnetization of Normal and Superfluid 3He

We have measured the thermodynamic magnetization in the various phases of normal and superfluid ³ He. The A-B discontinuity differs from that inferred from nuclear-specific (NMR) experiments. We offer reasons why this apparent disagreement can be consistent with our current picture of super-fluid ³ He. One consequence of this measurement is an improved set of values for the phenomenological Landau-Ginzburg free energy -parameters.