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.     

Superfluid density near the lambda point of4He under pressure

The superfluid density in ⁴ He was determined near T from the second-sound velocity as a function of T–T and pressure. The critical exponent of the superfluid density was found to depend, even slightly, on the pressure. Furthermore, the fundamental length ₀ in the coherence length = ₀ [1–(T/T)]^–' seemed to be proportional to the mean interatomic distance. The implications of the results are also discussed.This work was partly supported by The Ito Science Foundation and by The Nishina Memorial Foundation.     

Velocity of second sound and superfluid density near the superfluid transition in3He-4He mixtures

Using superleak condenser transducers, the velocity of second soundU ₂ has been measured near the superfluid transition temperature T in³He-⁴He mixtures with molar concentrationsX of³He of 0.0, 0.038, 0.122, 0.297, and 0.440. We have obtained the superfluid density _s/ fromU ₂ on the basis of linearized two-fluid hydrodynamics. The results for _s/ are consistent with those obtained from the oscillating disk method, as expected from two-fluid hydrodynamics. The value of _s/ at eachX could be expressed by a single power law, _s/=k, where =1-T/R, with the experimental uncertainty. It is found that the exponent is independent of concentration forX0.44 within the experimental uncertainty. This concentration independence of is in agreement with the universality concept. From the conclusion that the values of are universal forX0.44, the concentration dependence of the superfluid component _s is expressed by an empirical equation _s(X, )=²_s(0, ). It is found that corresponds to the volume fraction of⁴He in the superfluid³He-⁴He mixture. The value of is in agreement with that obtained from the measurement of the molar volume by others.This paper is based on a thesis submitted to Tokyo University of Education in partial fulfillment of the requirements for the Ph.D. degree.     

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.     

Acoustic Turbulence in Superfluid 4He

Recent work on nonlinear second sound wave propagation and acoustic turbulence in superfluid ⁴He is reviewed. Observations of direct and inverse turbulent energy cascades are described. The direct cascade arises due to the huge nonlinear dependence of the second sound wave velocity on its amplitude. The flux of energy injected at the driving frequency is transformed via successively higher harmonics until it is eventually attenuated by viscous dissipation at the short wavelength edge of the spectrum. The onset of the inverse cascade occurs above a critical driving energy density, and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomena is outlined and shown to be in good agreement with the experiments.     

Thickness measurements of unsaturated superfluid 4He films under driven and persistent flow

Third-sound techniques have been used to measure the thickness of an unsaturated superfluid ⁴He film as a function of flow velocity. Under the conditions of persistent flow the film thins according to the predictions of Kontorovich. In situations in which a heater is used to continuously drive a film current the measured thinning is in disagreement with the predictions of Kontorovich. A possible explanation for these results is presented. We conclude that the film thinning problem presents no fundamental discrepancy with the Bernoulli equation.Work supported by the National Science Foundation through grants DMR76-08260, 78-07762, and 79-09248.     

Solitons in superfluid 4He films

The Korteweg-de Vries (KdV) equation is derived from Landau two-fluid hydrodynamics applied to the thickness oscillation of the superfluid ⁴He film at low temperatures, where the main restoring force is van der Waals attraction from the substrate and the thermomechanical force due to phonons is a small correction. Since the usual third-sound generators and detectors are far wider than the individual solitons, the asymptotic solution of the KdV equation provided by the inverse scattering method is coarse-grained by regarding it as a continuous train of sharp pulses. The envelope so obtained still shows a singular front proportional to (t–t ₀)^–1/2, where t ₀ is the arrival time of the fastest soliton, and should therefore be observable with the appropriate experimental arrangement.     

Depression of the superfluid transition in4He

We study superfluid⁴He near T in a homogeneous metastable state where a finite superfluid velocity v_s is present. Neglecting vortices we perform a renormalization-group calculation of the critical velocity v_sc(T) at which the superfluid state becomes unstable. We apply this result to the situation where the superfluid velocity is induced by a finite heat current Q. A critical heat current Q_c(T) corresponding to v_sc(T) is found which implies a transition temperature T (Q)=T[1–A_oQ^x]. We determine the exact exponent x=[(d–1)v] ^–1 0.744 in d=3 dimensions and calculate A_o in one-loop order. Our results for A_o and x are compared with recent experimental data.     

Quantum Evaporation from Superfluid 4He

The quantum evaporation experiments of Brown and Wyatt ² have been re-analysed in the light of a recent measurement of the high-energy phonon spectrum created by a pulse-heated thin film ¹⁰ . Two sources of systematic error become significant at the level of the precision required by this new analysis: firstly, in the detector position which is recalibrated by using large-angle roton evaporation; and secondly, in the liquid height due to capillary action affecting the level-detectors. These effects have been included in an improved simulation of the experiment which has brought the angular dependence of the measured and theoretical phonon-atom evaporation results into agreement within the mechanical tolerances of the apparatus. The reanalysis suggests that the roton-atom evaporation probability increases with wave vector.     

Dispersion of ripplons in superfluid4He

The excitations of the free surface of liquid⁴He at zero temperature are studied, with special emphasis to the short wave length region. The hybridization mechanism between surface and bulk modes is discussed on a general basis, investigating the scattering of slow rotons from the surface. An accurate density functional, accounting for backflow effects, is then used to determine the dispersion of both bulk and surface excitations. The numerical results are close to the experimental data obtained on films and confirm in an explicit way the general reflection mechanism exhibited by rotons. Moreover they reveal the occurrence of a damped ripplon branch above the roton threshold.     

Superfluid density of3He measured by fourth sound

Superfluid density of³He has been measured using fourth sound in two superleaks: “confined,” packed powder and “open,” parallel channels. The superleak pore size has little effect on the superfluid density near the melting pressure, but it has surprisingly large effects at lower pressures. The open, parallel channel superleak results show an unexpected pressure dependence of “strong coupling” effects and an unexpectedly small superfluid density change at the B→A transition.     

Static response function in superfluid4He

Rigorous lower and upper bounds for the static response function in superfluid⁴He at zero temperature are derived using a sum rule approach. The ingredients needed to calculate the bounds are taken from recent Monte Carlo simulations for the ground state. The new bounds improve significantly the Feynman approximation and provide estimates of the static response function in agreement with the experimental data at zero pressure.     

Pulsed Nonlinear Sound in Superfluid 4He and 4He-3He Mixtures

Sound modes in ⁴ He and ⁴ He- ³ He mixtures which arise out of the two-fluid equations are made up up a vector convective flow and scalar temperature changes. A method for modeling nonlinear pulses of sound with geometric approximations to the vector and scalar components has recently been applied towards understanding nonlinear second sound near the lambda point. ⁶ The same method may be used, in general, for modeling linear and nonlinear sounds in Helium II. We demonstrate with a model for nonlinear second sound pulses in ³ He- ⁴ He mixtures and compare the results to experimental observations.     

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.     

One- and Two-Electron Bubbles in Superfluid 4He

Properties of one- and two-electron bubbles in superfluid ⁴He at 0 K were studied by density functional theory. The model allows for accurate treatment of both the electronic and liquid degrees of freedom and as such, enables accurate calculation of bubble energetics for the ground and excited electronic states. The obtained results were compared against the earlier “bubble model” calculations and the limits and accuracy of the bubble model were established. The calculations were carried out in 3-D space and the non-spherical solvation structures for the 1P and 1D excited states were calculated. The 1P state was found to be stable within the radiative lifetime and no plausible non-radiative relaxation channels were found. Finally, a coupled boson and fermion density functional theory was used to show that two-electron bubbles are unstable in both the singlet and triplet electronic states.      

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.     

Persistent currents in saturated superfluid4He films on rough surfaces in the presence of third-sound resonances

We have measured persistent current film flow through a long, stainless steel tube by Atkins oscillations between reservoirs at the tube ends and by Doppler-shifted third-sound resonances within the saturated film. Qualitatively the surface roughness is observed to both raise the Atkins oscillation frequency and lower the third-sound phase velocity from that expected for an ideal surface but otherwise has little effect on the motion. The third-sound resonance frequencies are shown to shift with the square of the persistent current velocity by an amount predictable using two-fluid hydrodynamics. The presence of the third sound does not affect the stability of the persistent currents in these thick films. The third-sound phase velocity is observed to have a temperature dependence consistent with (_s/)^1/2(1 + TS/L) as predicted by Bergman.Supported by the National Science Foundation.Alfred P. Sloan Research Fellow.     

A possible explanation for the discrepancy in electron persistent current amplitudes: A superfluid persistent current analog

Recently there has been considerable interest in normal electron persistent currents which result from the wave nature of electrons in a normal metal ring for which inelastic electron-phonon scattering has been reduced so that the electron maintains phase coherence around the ring. The application of the current theory of electron transport, which includes the effects of elastic scattering in a disordered potential field, produces an expression which disagrees with the experimental measurements by Webb, et al. In this paper we present an acoustic analog of wave mechanical electrons in a disordered circular waveguide and derive an expression which agrees with the results of the electron persistent current measurements. The acoustic analog shows that the expression derived from electron transport is also correct, but only under conditions which do not correspond to the actual method used in measuring the electron persistent currents. A proposed experiment to test the model using superfluid helium in a disordered scattering field will be presented.     

The Superfluid 4He Analog of the RF SQUID

We describe the theory, design, fabrication, and performance of a super fluid ⁴ He device which is the analog of the superconducting RF SQUID. This device is a sensitive rotation detector and is used to sense the rotation of the Earth. We also describe the experimental developments and observations which lead to the construction of this successful device.