Size effects in He II as measured by fourth sound

Fourth-sound measurements are used to determine the depletion in the superfluid density _s which occurs in the helium filled small pores of packed powders. The measurements also give the reduction in superfluid onset temperature. The pore size distribution of several samples was determined from desorption isotherms. Using this distribution and an independent pore model, calculations based on the Ginzburg-Pitaevskii ansatz with a healing length first proposed by Mamaladze are found to be in good agreement with experimental results in several cases. The superfluid onset temperature seems to be determined by the average pore size. Fourth-sound measurements as a function of temperatureT in large pore geometries accurately give _s (T –T)^2/3 in the neighborhood of the lambda temperatureT .     

Superfluid density and critical current of3He in confined geometries

Superfluid³He in severely confined geometries is studied in the Ginzburg-Landau limit. Both A and B phases are analyzed in narrow slabs and in small cylinders. Physically measurable quantities include the superfluid density and the critical current, which are significantly suppressed by the boundaries. Related alterations in the phase diagram are also considered. For small lateral dimensions, the A phase can be favored even well below the polycritical pressure.     

Effects of4He coverage on the propagation of fourth sound in superfluid3He

We report measurements on the effects of⁴He coverage and pressure on the fourth sound propagation in superfluid³He in confined geometries of four different pore sizes.     

The effect of a magnetic field on fourth sound in 3He

The influence of a magnetic field on the propagation of fourth sound in superfluid ³He is studied. The field and temperature dependences of the average superfluid density \- _s / and fourth sound Q are measured. The field dependence of \- _s / is very different in a porous medium than predicted by Ginzburg-Landau theory applied to bulk liquid. In particular, a magnetic suppression of \- _s / is observed in the temperature and pressure ranges corresponding to the A phase in bulk liquid. There is strong evidence of a magnetic suppression of T _c itself. The measured \- _s / has a slight history dependence in a magnetic field, but none in zero field. The fourth-sound Q values are compared to the theoretical work of Smith, Jensen, and Wolfle. Quantitative confirmation of their work is problematic.     

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     

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.     

Doppler shift in third and fourth sound in 3He-4He mixtures

The Doppler-shifted velocity of third sound in a system where the superfluid flows with velocity v _s is given. The calculations are to first order in v _s/u₃ where u ₃ is the third-sound velocity in the rest frame. We take into account the effects of the pressure and ³He concentration gradients normal to the substrate. Corresponding calculations for fourth sound are also given.Supported in part by the GFK, West Germany, through the Israel National Council for Research and Development.     

Dissipative Coefficients of Spin-Polarized Superfluid 3He

The attenuation of second sound (spin-entropy) wave in superfluid A ₁ -phase has been measured in magnetic fields up to 11 tesla and to sufficiently high frequency to observe the bulk attenuation proportional to the square of frequency. A comprehensive test on the existing theories of hydrodynamics and dissipative coefficients can be made with the measured attenuation coefficient. The spin diffusion coefficient plays a major role in the attenuation. The observed excess attenuation is discussed in terms of the temperature dependent spin diffusion coefficient in the superfluid.     

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     

Measurement of Superfluid 3He Film Flow by Inter-digitated Capacitors

We report the measurements of the critical current of superfluid ³He film for the thickness of 0.47 µm. By employing inter-digitated capacitors, 2.5×10^?2 mm^{3 3}He can be manipulated with 0.4% resolution. Critical current J ^f _c of superfluid ³He film were observed for the onset of dissipative flow. The magnitude of measured J ^f _c is considerably smaller than the theoretically predicted pair-breaking critical current. This resugt indicates that another mechanism must participate in the dissipation of superflow.     

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.     

Superfluid Transition of a 4He Thin Film Pressurized by Bulk Liquid 3He

We measured transverse acoustic impedance Z of normal fluid ³He at 46.6 MHz on a surface coated with a thin ⁴He film. The real component of the impedance, Z′, in the coated samples deviates from Z′ in the pure ³He in the low temperature region. Z′ on the coated samples is almost identical with Z′ in the pure sample at high temperature and gradually deviates below a particular temperature T _onset . T _onset  is possibly the superfluid onset temperature of the ⁴He film pressurized by the bulk liquid ³He. The gradual decrease in Z′ means that the superfluid component in ⁴He film increases gradually, which is expected from the dynamic KT transition at high frequency. The thicker is the film, the higher is the T _onset . The range of T _onset we observed was between 40 and 160 mK. This is much lower than that at the saturated vapor pressure. Suppression of T _onset achieved by the applied pressure from bulk liquid ³He was presumably caused by the dissolved ³He in the film, thickening of the inert layers and/or by the strong correlation effect. The result shows that the specularity of ³He quasiparticle scattering is strongly affected by superfluidity of the ⁴He film.     

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.     

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.     

Anisotropic Aerogels for Studying Superfluid 3He

It may be possible to stabilize new superfluid phases of ³He with anisotropic silica aerogels. We discuss two methods that introduce anisotropy in the aerogel on length scales relevant to superfluid ³He. First, anisotropy can be induced with uniaxial strain. A second method generates anisotropy during the growth and drying stages. We have grown cylindrical ∼98% aerogels with anisotropy indicated by preferential radial shrinkage after supercritical drying and find that this shrinkage correlates with small angle x-ray scattering (SAXS). The growth-induced anisotropy was found to be ∼90° out of phase relative to that induced by strain. This has implications for the possible stabilization of superfluid phases with specific symmetry.     

Vortex Generation in Superfluid 3He by a Vibrating Grid

Recently we have found that a vibrating wire resonator produces turbulence in superfluid ³He-B at low temperatures when driven above its pair-breaking critical velocity. The vorticity is produced along with a beam of excitations from pair breaking. Here, we discuss preliminary measurements of turbulence generated from an oscillating grid at low temperatures. The grid oscillator is made from a goal-post shaped vibrating wire resonator supporting a fine copper mesh. While the dissipation by a conventional wire resonator is dominated by pair-breaking at the velocities required for turbulence generation, the dissipation of the grid oscillator appears to be dominated by turbulence. This allows us to generate turbulence without the unwanted effects of a quasiparticle beam. Preliminary measurements suggest that the grid turbulence has a rather different behaviour from that generated by conventional wire resonators.     

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.