Faraday Instability on a Free Surface of Superfluid 4He

We observed that the Faraday waves were parametrically generated on a free surface of superfluid ⁴He. Our sample cell was supported by plate springs and had a permanent magnet on the top. It was oscillated by applying oscillating current to a superconducting coil. We prepared the sample cell made of polycarbonate so as to optically observe the superfluid surface. Standing wave patterns appeared on the surface and their frequencies were one half of a driving frequency. We observed clear threshold amplitude of the oscillation for the instability. Threshold is usually determined by the viscosity of fluid and thus there must be a dissipation mechanism in superfluid for the threshold.     

Scattering of Elementary Excitations at the Surface of Superfluid 4He

We study the scattering of atoms, rotons and phonons at the free surface of superfluid ⁴ He. We calculate the evaporation, condensation and reflection probabilities in the framework of linearized time dependent density functional theory accounting for elastic one-to-one processes. We explore the angular dependence of the scattering probabilities showing that most results are independent of the incidence angle and can be expressed in terms of a single energy dependent parameter.     

Anisotropy of Superfluid 3He Near Free Surface Investigated by Surface State Electrons

We have measured the resistivity of a Wigner solid formed on the free surface of superfluid ³He in the A and B phases under magnetic fields. The mobility of the Wigner solid is limited by the collisions of thermally excited quasiparticles in ³He, and hence is very sensitive to the distribution of quasiparticles in momentum space. The observed resistivity of the Wigner solid in the A phase asymptotically approaches the temperature-square dependence at low temperatures, reflecting the A phase gap with point nodes. Its temperature dependence is well explained by the vector being uniformly aligned normal to the surface. The resistivity in the B phase, in contrast, exhibits an exponential decrease at low temperatures. The resistivity in the small field well agrees with the behavior expected for the isotropic gap in the BW state. The resistivity increases in high magnetic fields, which is explained by the combination of the distortion of the gap in the BW state by the field and the orientation of the order parameter caused by the free surface.      

Surface tension of liquid3He and4He near the liquid-gas critical point

The surface tension of liquid³He and⁴He was measured near the gas-liquid critical points in the reduced temperature range 3×10^–4–1, where t (T _c –T)/T _c . The critical exponents were found to be ₃=1.289±0.015 for³He and ₄=1.306±0.017 for⁴He. These values are very close to those for classical liquids, and are consistent with the value of 1.28 predicted by Widom, but are apparently different from the exponents previously obtained for liquid helium isotopes, which are near unity. The critical coefficients show good agreement with the quantum-corrected corresponding states theory for the Lennard-Jones 6–12 potential discussed by Young. The interface thickness is deduced from Widom's theory to bed=d ₀t^–v withd ₃₀=0.14±0.03nm and v₃=0.57±0.04 for³He, andd ₄₀=0.37±0.07 nm and v₄=0.58±0.01 for⁴He.     

Surface Magnetism of Liquid 3He on 4He Pre-plated Graphite

No Heading The nuclear susceptibility of liquid ³He in Grafoil pre-plated by 2.5 and 3.5 layers of ⁴He has been studied with a cw NMR method at temperatures between 0.7 and 100 mK under various liquid pressures. The 3.5 layers of ⁴He pre-plating suppresses a formation of the first and second solid ³He layer, eliminating most of surface magnetization at saturated vapor pressure. However, with increasing liquid pressure, a magnetization obeying a Curie Weiss law gradually grows in the same way as in the previous experiment for pure liquid ³He. This magnetization, induced by pressurization, is attributable to the formation of solid ³He layer above the pre-plated ⁴He.PACS numbers: 67.80.Jd, 75.70 Cn, 67.70.+n.     

Viscosity and Mean Free Path of Very Diluted Solutions of 3He in 4He

We have measured the laminar friction of various diluted ³ He- ⁴ He mixtures, of natural ⁴ He and of isotopically pure ⁴ He on an oscillating sphere below 1 K. For ³ He concentrations x ₃ ranging from 10 ^–2 to 10 ^–4 we find a reduction of the drag above 0.5 K when compared to the pure liquid and a large enhancement below, which is almost independent of x ₃ . At low concentrations 5·10 ^–5 >x ₃ 5·10 ^–7 the drag becomes proportional to x ₃ which implies a transition from a hydrodynamic to a ballistic regime. This is confirmed by deducing the mean free path of the ³ He atoms from the data. The temperature dependence of the drag in the ballistic regime, however, is found to be proportional to T and therefore different from the expected T ^1/2 behaviour.     

Surface tension of liquid4He. Surface energy of the Bose-Einstein condensate

The surface tension of liquid⁴He was measured by means of surface-wave resonance, and the relative variation showed excellent agreement with that previously obtained by a precise capillary-rise method. The absolute value of the surface tension at absolute zero was measured as 354.4±0.5 mdyne/cm, 6% smaller than the previous value. The surface energy associated with the Bose-Einstein condensate wave function was found to dominate the surface tension in the superfluid phase. The condensate fraction other than in the vicinity of the point was estimated asn ₀(0)-n ₀(T)=A(T/T ), withn ₀(0)=0.125±0.025,A=0.177±0.047, and =5.07±0.17.     

Absolute Value of the Surface Tension of Liquid 4He

In 1985 Iino et al. [J. Low Temp. Phys. 61, 155 (1985)] measured the surface tension of liquid ⁴ He by the surface-wave resonance method, and reported that the surface tension at 0K is 354 N/m. Recently, Roche et al. [J. Low Temp. Phys. 106, 565 (1997)] obtained the absolute value at 0K to be 375 N/m from the dispersion relation of a capillary wave at a micron wavelength. There is a 6% discrepancy between those two values. To determine the meniscus effects for the surface waves and the absolute value of the surface tension, we measured the resonance frequencies of the surface wave in two parallelepiped cavities with different widths. By comparing the same wave number of the two cavities, it was found that the resonance frequencies are shifted to be slightly smaller by the meniscus effects. The absolute value of the surface tension, which was obtained by eliminating these effects by using the resonance frequencies of the two cavities, was in agreement with that of Iino et al.     

Surface tension and mass density of dilute solutions of4He in3He

We report the first precise measurement on the surface tension of dilute solutions of⁴He in³He from 2.6 K to the phase separation temperature as well as the mass density of the solutions. Compared to liquid³He, the surface tension of dilute⁴He solutions increases by 3.5 ± 0.1 mdyne/cm for 2.5%⁴He and 7.4 ± 0.2 mdyne/cm for 5.2%⁴He at 1 K. The increase of the surface tension means a negative adsorption, i.e.,⁴He atoms are excluded from the free surface. The surface adsorption, which is calculated on the basis of the⁴He quasiparticle model, was compared with the data. Assuming that the effective potential near the surface for the⁴He quasiparticle is long-range, the temperature dependence of the surface adsorption is well explained.     

Plasma Resonance of the Wigner Solid on the Free Surface of Normal and Superfluid 3He

The Wigner solid on liquid ³ He is used as a sensitive probe for the study of the surface dynamics. We have experimentally investigated the behavior of optical coupled plasmon-ripplon (CPR) resonances for temperatures down to 0.4 mK. We have used a linewidth of CPR resonance f for getting = (2f)^–l, the collision time in the scattering of surface electrons from the surface roughness. The collision time is in good agreement with single-electron-ripplon scattering theory down to 30 mK, while below 30 mK the collision time deviates from the theory, and at 1 mK experimental value of is one order of magnitude longer than the theoretically predicted one.     

Surface Effects of 4He Coating on the Viscosity and the Slip Length of Normal and Superfluid 3He

We have measured the viscosity, , and the slip length, , of normal and superfluid ³ He using a torsional oscillator with a thick sample space. We coated the oscillating surface with 2.5 layers of ⁴ He film to study how the ⁴ He thin film changes the scattering mechanism of ³ He quasiparticles at the cell wall at 5 bar and 21 bar. In the normal phase, the temperature dependence of the viscosity was changed a little by the ⁴ He film at 21 bar but no change was observed at 5 bar. The slip length was enhanced by ⁴ He coating at 5 bar. This enhancement indicates the increase of specularity of ³ He quasiparticles scattering at the oscillating surface. On the other hand, a reduction of the slip length was observed at 21 bar. In the superfluid phase, the temperature dependence of supports the existence of Andreev reflection even with ⁴ He film on the surface at 5 bar and 21 bar.     

Surface tension of liquid3He at low temperature

The thermal contribution to the surface tension of liquid³He due to the single quasiparticle motion is estimated in the low-T regime using a local approximation for the entropy. The density and temperature dependence of the effective mass is shown to play a crucial role in determining the behavior of (T). The theoretical predictions explain the anomalous behavior of (T) recently observed at low temperature by Suzuki et al.³ Predictions for the temperature dependence of the interfacial tension of liquid³He-⁴He mixtures are also given.     

State of the4He film at monolayer completion

We calculate the density of⁴ He at which a monolayer completes when adsorbed at zero temperature on a hypothetical substrate (characterized by the potential well depthD and the gas-surface dispersion coefficientC ₃). In the case of an alkali metal substrate, the monolayer is fluid; otherwise, it is a two-dimensional solid, except for H₂, which is a borderline case. We discuss the prospects for monolayer superfluidity.     

Fluctuations above the superfluid transition in liquid3He

It is shown that fluctuations above the superfluid transition in liquid³He depend strongly upon the relative angular momentum1 for which Cooper pairing occurs. The effects may be calculated for any value of1 and they should be observable in the static magnetization, viscosity, and spin diffusion coefficient, giving a means of determining1. Conclusions to be drawn from existing experiments are discussed.Work supported by Energy Research and Development Administration.     

Effective Free Energy for Solidification of Superfluid 4He Under Pressure

Effective free energy for the solidification of the superfluid ⁴ He under pressure is presented. Since this free energy is a function of two parameters, the density change and the translational symmetry breaking parameter , it is expected to describe over both the superfluid phase and the solid phase.The experimentally established values below and equal to the melting pressure P_m are successfully reproducible by the free energy. For P>P_m, where the superfluid is metastable, the free energy predicts that the instability for should occur first and then accompanies. That is, -nucleation is essential for the solid nucleation in the superfluid ⁴ He.     

Fluctuations in small volumes of liquid 3He

We calculate fluctuation contributions to the thermodynamic properties in a small volume of liquid ³He. Functional integration techniques are employed to derive the fluctuation free-energy functional for temperatures just above the superfluid transition temperature and for zero temperature. Due to finite-size effects, the critical regime is estimated to be large enough to warrant an experimental observation of fluctuations. At zero temperature we find two kinds of quasicollective gapless excitations, which correspond to fluctuations of phase and rotations of the order parameter in spin space, respectively. These excitations result in a periodic time dependence of the pair correlation function. Finally, the experimental observability of the effects considered are contemplated.     

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid ³He and (for the first time) to liquid ⁴He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid ³He, it is found that S-wave scattering dominates for wave number k<0.5 Å^?1. At the Fermi momentum k _F, the effective partial cross section σ _? (and thus the total cross section σ _T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 Å^?1, the effective total cross section is nearly constant. On the other hand, it is found in liquid ⁴He that S-wave scattering dominates for k<0.3 Å^?1, and a peak exists in σ _T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the ?=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the ³He gas. It is, therefore, a purely many-body effect in liquid ³He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.     

Trapping Electrons in Electrostatic Traps over the Surface of 4He

We have observed trapping of electrons in an electrostatic trap formed over the surface of liquid ⁴He. These electrons are detected by a Single Electron Transistor located at the center of the trap. We can trap any desired number of electrons between 1 and ∼30. By repeatedly (∼10³–10⁴ times) putting a single electron into the trap and lowering the electrostatic barrier of the trap, we can measure the effective temperature of the electron and the time of its thermalisation after heating up by incoherent radiation. E. Rousseau’s present address: Ecole Centrale, Paris, France. D. Ponarine’s present address: Chemistry Dept., North Carolina State Univ., Raleigh, NC 27695, USA.