Measurements of superfluid densities and critical superfluid mass currents of pure 4He and 3He/4He mixtures in nuclepore near the lambda transition

Measurements have been made of the relative superfluid density _sp/ and the critical mass current I _sc for the onset of dissipation in the superfluid flow of pure ⁴He and ³He/⁴He mixtures in the circular cylindrical pores of Nuclepore near the transition, using a double-ended Helmholtz resonator. Pore diameters of 0.03, 0.1, and 0.4 m were studied using ³He mole fractions of 0.0,0.2, and 0.4. For each pore diameter d _p and mole fraction x our results for _sp / were fitted relatively well by the form C(t – t ₀₁)^0.675 and those for I _sc by the form I _sc0(t–t _0c ) ^g , where t [T –T]/T . For each combination of d _p and x the reduced onset temperatures t ₀₁ and t _0c are in rough agreement with each other but somewhat larger than values found by others for Nuclepore. For the smaller two pore diameters, these onset temperatures are consistent with the universality hypothesis that near T, ² _sb /m ₄ ² k _B T should be a constant independent of T and x. Here is the reduced Planck constant, _sb is the bulk superfluid density, is the coherence length, m ₄ is the ⁴He atom mass, k _B is Boltzmann's constant, and T is the absolute temperature. At each value of x the amplitudes C agree well with the corresponding amplitude for _sb /, and g equals 1.17 ± 0.04 for all cases. Measurements of the velocity of second sound at x = 0.000, 0.190, 0.401, and 0.450 are also reported.Work supported by U.S. Department of Energy contract EY-76-S-02-1569.     

Frequency dependence of superfluid onset temperature of4He films on oscillating substrates

We have studied the frequency dependence of the superfluid onset for⁴He films on Mylar substrates using a two-torsional-oscillators technique. A peak of the dissipation accompanied by the superfluid onset appears at higher temperatures for 2009 Hz than for 530 Hz. The temperature difference T_p between the two peaks is 2.0 ± 0.5 mKfor coverages with the onset temperature T_c of 1.4 K, and increases by a factor of three with decreasing T_c from 1.4 to 0.95 K. In the temperature dependence of the dissipation, the dissipation width also increases by a factor of three with decreasing T_c from 1.4 to 0.95 K. The T_c dependencies of T_p and the dissipation width indicate that an intrinsic parameter D/r₀ ² of a vortex decreases with the superfluid onset temperature, where D is a diffusion constant and r₀ a core radius.     

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.     

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.     

Study of rotons in superfluid4He by Raman scattering

There is a long standing disagreement between neutron and Raman scattering from rotons in superfluid⁴He near T. In neutron scattering the linewidth becomes very large and the roton signal seems to disappear at T. A substantially smaller linewidth is observed with Raman scattering and the roton signal is present even at T. We have interpreted this difference (J. Low Temp. Phys. 93, 879 (1993)) as due to a modulation of the roton energy by a fluctuating local superfluid velocity due to proliferation of vorticity as T is approached. This gives rise to an extra contribution to the roton linewidth in neutron scattering but not in Raman scattering in which two rotons with almost opposite momenta are excited. We propose a test of this explanation with evanescent field Raman scattering. It has been suggested (A. Kuklov, A. Bulatov and J.L. Birman, Phys. Rev. Lett. 72, 3855 (1994)) that in such a measurement the scattering by a single roton should be measurable. In this case the presence of a fluctuating local superfluid velocity should show up as in neutron scattering and corroborate our proposal.     

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.     

Variational theory of rotons in superfluid4He

We have extended the shadow wave function for excited states by including an explicit backflow term in the shadow variables. The variational computation gives a roton energy 9.18 K, only 6% above experiment. Similar agreement is found at freezing density. Also the strength Z_q of the single excitation peak greatly improves. The uniform agreement between theory and experiment at all wave vectors suggests that there is no qualitative difference in the wave function of phonon, maxon and roton excitations. Only the amount of backflow and short range correlations greatly varies with k.     

Heat transport in dilute mixtures of3He in superfluid4He

We report new measurements of the effective thermal conductivity K_eff and relaxation time τ in dilute mixtures of³He in superfluid⁴He, with molar concentrationsX≤10⁻³. The temperature range extended fromT≈1.4 K toT _λ. Both K_cff and τ are found to agree with theoretical predictions, in contrast to previous experiments where significant differences were observed. A new thermal conductivity cell design was used which almost completely eliminates extraneous volumes and surfaces, and the earlier results are explained in relation to these design changes.     

Second-viscosity phenomena in dilute solutions of3He in superfluid4He

A theory of second-viscosity phenomena in dilute solutions of³He in superfluid⁴He is presented. The theory considers only phonon and³He quasiparticle excitations and is therefore valid at temperatures below about 0.6 K. It is shown, by an exact calculation, that within the framework of the Landau-Pomeranchuck model for the³He quasiparticle excitation energy, the four second-viscosity coefficients are related to one another and that only one of them is actually an independent kinetic coefficient. The relations between the second-viscosity coefficients are applied to analyze the expressions for the dissipative function and the first- and the second-sound attenuation coefficients. It is shown that the second-viscosity contribution to the second-sound attenuation is smaller by an order of magnitude than its contribution to the first-sound attenuation.     

Multiple quantum phase slips in superfluid4He

Phase slips by 2 in the critical flow of superfluid 4He through an orifice have been known to exist for some time. Besides these small, regular events, large and precipitous drops of the velocity which may cause up to a full collapse of the flow through the orifice have been observed by a number of authors. We have found that collapses are robust and repeatable features during the same cool-down and correspond to events involving n quantized vortices. They depend on temperature, pressure, 3He content and resonator drive level. At a given pressure, their appearance is governed solely by the magnitude of the superfluid velocity vs.     

Mean free path effects in superfluid4He

The mean free path effects in superfluid He II was studied with a vibrating wire method in the temperature range from T down to 20 mK under the saturated vapour pressure. The transition from the hydrodynamic regime to the ballistic regime was clearly observed at around 0.7 K with a 47 µm diameter wire. In the hydrodynamic regime the usual Stokes' approximation was found to be insufficient to interpret the results. In the ballistic regime the results can be explained quantitatively with the kinetic theory of phonons. However, below about 0.15 K there appear non-linear effects such as the distortion of the resonance line shape and a hysteresis behavior, which become stronger with decreasing temperature.     

Solitary waves in saturated films of superfluid 4He

It is shown that there should exist in saturated films of superfluid ⁴He at low temperature a nonlinear surface wave described by the Korteweg-de Vries equation. The effect of surface tension makes the solitary wave cold, in contrast to very thin films discussed in a preceding paper. An electrostatic method is proposed to generate cold solitary waves. The asymptotic behavior can be found theoretically by the inverse scattering method. Estimates of parameters imply the possibility of observing each solitary wave separately.     

Thermometry using the osmotic pressure of mixtures of He3 in superfluid He4

Recent measurements of the osmotic pressure of mixtures of He³ in superfluid He⁴ demonstrate the feasibility of temperature measurement using either of two experimental techniques. The first method, developed by H. London, measures the osmotic pressure of the saturated mixture and is useful for thermometry down to 30 mK. The second method, discussed in this paper, uses very dilute mixtures and is useful down to 10 mK.     

Time-dependent thermal convection in dilute solutions of 3He in superfluid 4He

Time-dependent thermal convection can occur in a unity-aspect-ratio Rayleigh-Beard convection cell containing a dilute solution of ³He in superfluid ⁴He when the fluid is heated from above. Results are presented primarily for a 0.24 mole % He solution at 0.925 K. Means is provided for introducing heat at the top and separately for a central plug and an outer ring such that both are at a constant temperature gDT above the bottom. A critical temperature difference T _cfor convection can be defined above which both steady and time-dependent convection occur. The time-dependent effects include a region of T. near T _cand characterized only by excessive noise, a region of somewhat higher T where there are intermittent major changes in the plug heating rate with a time distribution like that for random events, and a region at still higher T where periodic but nonsinusoidal variation of the heat flow is observed. When a long enough time, several months, has elapsed after cooling down the apparatus, time-dependent states no longer occur, and the heat flow above T _cis limited to steady convection. Briefly raising the temperature of the apparatus to 77 K is sufficient to restore the possibility of time-dependent states.     

Recent progress in the theory of rotons in superfluid4He

The excitation spectrum of superfluid ⁴ He is discussed on the basis of a shadow wave function. The potential and kinetic energies of the excitations are computed at different densities. The theory has been extended at finite temperature and we obtain the roton contribution to the radial distribution function, to the depletion of the condensate and to the dynamical structure factor S(q,). We present also the first realistic microscopic computation of the roton energy at finite T. Possible role of thermally excited vortices on rotons is considered. With a simple model we show that some discrepancies between the linewidth of the roton response in neutron and in Raman scattering can be resolved.     

Generation of superfluid vortex turbulence by high-amplitude second sound in4He

High-amplitude second sound in superfluid⁴He is used to generate vortex turbulence. By the use of a novel resonator designed to avoid nonlinear effects, a steady-state ac counterflow field is produced with amplitudes high enough to generate the turbulent state. The transition to the turbulent state shows hysteresis similar to that observed in dc superflow measurements. Critical velocities were measured as a function of both temperature and frequency. The frequency dependence agrees with the predictions of dynamic scaling theory, and the temperature dependence is the same as that observed in dc counterflow experiments.