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.     

Sound attenuation and3He-3He interaction in3He-4He liquid mixtures at saturated vapor pressure

The interaction potential between³He quasiparticles in³He-⁴He liquid mixtures is determined from the sound attenuation at saturated vapor pressure. Sound attenuation was measured in mixtures with³He mole fraction ranging from 0.0289 to 0.0573. The superfluid transition temperature of³He in mixtures and other properties were then estimated from the deduced interaction potential.     

Ultrasonic measurements as a probe of3He/4He phase separation in aerogels

We have used ultrasonic velocity and attenuation measurements to study the phase separation of³He/⁴He mixtures confined in a silica aerogel with a porosity of 87%. We used both shear and longitudinal sound and varied the frequency between 4 and 20 MHz. The superfluid transition is accompanied by a velocity increase due to decoupling and by a critical attenuation peak which increases with frequency. At the phase separation there are changes in the velocity and attenuation, and hysteresis on thermal cycling. We show some recent results and discuss how they relate to the phase diagram inferred from torsional oscillator and heat capacity measurements on helium mixtures in aerogels.     

Acoustic Properties of Normal Liquid 3He in 98% Aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation and sound velocity measurements in the normal state of liquid ³He in 98% aerogel. The absolute attenuation and sound velocity were determined by direct propagation of sound pulses through the medium in a wide range of temperatures, 2 mK<T<200 mK. Due to the scattering off the aerogel, the sound excitation remains as first sound over the entire range of temperatures and pressures studied. Unlike pure liquid ³He, the sound attenuation shows a minimum around 30–50 mK, depending on the pressure. We report our results of absolute sound attenuation measurements at 29 bars of sample pressure.     

Sound attenuation in3He-4He liquid mixtures under pressure

The attenuation of sound was measured in³He-⁴He mixtures with³He concentrations ranging from 2.89 to 8.03% at pressures of 10 and 20 bar. The quasiparticle interaction potentials were then determined at each pressure by analyzing the sound attenuation data. The superfluid transition temperature of³He and other properties in the mixtures were then estimated from the interaction potentials.     

Decoupling of 3He Films Adsorbed on Two-Dimensional Mesoporous Hectorite

The mechanical responses of physisorbed films to the vibration of a substrate were investigated by measuring the sound velocity and attenuation of a two-dimensional mesoporous hectorite. The sound velocity of a pellet with adsorbed ³ He films increased drastically at low temperatures accompanied by the attenuation. The temperature dependence of the sound velocity and attenuation can be described by the thermally activated relaxation process, and the increase in sound velocity was found to be proportional to the amount of adsorbed ³ He. The most plausible explanation for this behavior is that ³ He films decouple from the vibrating substrate at low temperatures.     

The solubility of spin-polarized3He in4He and the superfluidity of3He in3He-4He mixtures

We investigate the possibility of a large enhancement of the T = 0 finite solubility of³He in⁴He due to spin-polarization. The size of the effect depends on the fraction of³He atoms in the system. We present two different approaches for the limits of a small and a large number of³He atoms compared to the number of⁴He atoms. Since the possible³He superfluid phase transition depends on³He density, we calculate the consequences of this change in the solubility for its superfluid transition temperature. It is shown that for small fractions of³He, the transition temperature is enhanced mostly due to the enlargement of the up-spin Fermi sphere. In the opposite limit the transition temperature is enhanced as a result of the increased³He solubility.     

Absolute Ultrasound Attenuation Measurements in Superfluid 3He in 98% Aerogel by Direct Transmission

Systematic investigations on the effect of static disorder on p-wave superfluid ³He have been made possible by utilizing the unique structure of high porosity silica aerogel. For the past 10 years, a burst of experimental efforts revealed that three distinct superfluid phases exists. We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B-phase of the superfluid ³He in 98% aerogel. The absolute attenuation was determined by direct propagation of sound pulses through the medium in a wide range of temperatures, down to 200 μK, for sample pressures of 10 and 29 bars. Our results provide direct information on the zero-energy density of states of the superfluid phase in aerogel originating from impurity scattering.     

Transverse Ultrasound Measurements in 4He Single Crystals

Recently, Kim and Chan (Science 305:1941, 2004; Phys. Rev. Lett. 97:115302, 2006) have reported an anomalous decoupling transition of solid ⁴He in a torsional oscillator measurement, and interpret their results as evidence for non-classical rotational inertia and a possible supersolid phase of ⁴He. The detailed nature and properties of such a “supersolid” state in ⁴He are still far from being clear, although there are clues from experiments involving ³He impurities, different sample cell geometries, annealing effects and grain boundary flow. Defects produced during crystal growth or deformation (e.g. dislocations) may affect supersolidity, or even produce it, and they are expected to have significant impact on the elastic properties of the solid. The supersolid fraction could also decouple from the lattice and produce a decrease in the transverse sound speed. We have begun the experiments in this laboratory to study such effects, measuring the velocity and attenuation of transverse ultrasound at 10 MHz in ⁴He single crystals grown at constant pressure.      

3He Impurity Effects on the Growth Kinetics of 4He Crystals

We report the growth kinetics of the⁴He crystals with a small amount of³He impurities around 0.8 K. The growth resistance was measured using the response of the charged interface with respect to an externally applied voltage. In 5 ppm and 10 ppm³He mixtures, it is found that (1) the relaxation process can be expressed as an exponential behavior, (2) the growth resistance becomes larger compared to pure⁴He and does not have a strong³He concentration dependence, and (3) the temperature dependence of the growth resistance is much the same as pure⁴He. We discuss several possible explanations of the present experiment.     

Supersaturation and Nucleation in Superfluid 3He–4He Solutions under Elevated Pressures

Nucleation and phase separation kinetics of superfluid ³ He– ⁴ He solutions at various pressures and concentrations were investigated. The measurements of the first sound velocity and the attenuation as well as the liquid dielectric constant determination were used. The study was performed at a constant temperature and pressure and the phase transition was initiated by continuous increasing the ³ He concentration. It is shown that the pressure dependence of the attainable supersaturations is non-monotonic when passing through a maximum at pressure of about 0.1 Bar. The comparison has discovered great differences between the results obtained and theoretical predictions.     

Recent Progress in Thin 3He–4He Films

We review recent work on the properties of ³He–⁴He thin film mixtures. The subject is introduced by reviewing the contributions made by Gasparini and co-workers. In the first part of this survey, we examine a microscopic calculation of the effects that an adsorbed ³He component has on the collective excitations associated with a ⁴He film, third sound. The work in question computes the change in the third sound velocity due to adding ³He, and we can compare this with existing experiment. For small ³He coverage, the change in the third sound speed depends on the derivatives of the species chemical potentials with respect to the areal density. The microscopic calculation shows oscillations in the third sound speed that reflect the layered structure of the film. In the second part of this survey, we concentrate on the ³He component. An important impact of the ⁴He environment is to change the bare mass in the limit of zero ³He concentration to a hydrodynamic mass. Quasiparticle interactions are introduced through the Landau parameters. Our Landau parameters are determined by fitting s-wave and p-wave T-matrix components using experimental results for the effective mass and the spin susceptibility. We can then predict the thermodynamic behavior of the mixture films at finite polarization, and in addition we can predict the spectrum of zero-sound excitations at all polarizations.     

Specific heat of amorphous3He films and confined liquid3He

We have measured the heat capacities of³He films and liquid³He in porous Vycor glass at 10 to 600 mK. With increasing the film thickness from 1 to 3 atomic layers, the specific heat evolves gradually from that typical to solid to that of liquid³He. At about 2 atomic layers, however, its low-temperature part is nearly temperature-independent; we interpret this as a result of gradual freezing of spins in an amorphous solid³He film with decreasing the temperature. The contribution of liquid³He in the center of the Vycor pores can be described as the specific heat of bulk liquid³He at corresponding pressures in the range 0 to 28 bar. The thickness of amorphous solid on the pore walls increases with external pressure roughly linearly. Preplating the walls with⁴He allows to determine the positions of³He atoms contributing to the surface specific heat at 10 to 50 mK. In addition, the contribution from the specific heat of³ He -⁴He mixing at 100 to 600 mK is discussed as a function of pressure and amount of⁴He.0n leave from ISSP Acad. Sci. of Russia, Chernogolovka, Russia     

Bound states of3He in3He-4He mixture films

³He atoms dissolved in super fluid⁴He may form aimers (³He)₂ in twodimensional (2D) geometries. We study dimer formation in films of dilute³He-⁴He mixture. After designing a schematic³He-⁴He interaction potential we calculate the dimer binding energy for various substrates. It is shown that³He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.     

Distribution of 3He–4He Mixtures in a Bi-Porous System

We have investigated the distribution of ³He–⁴He mixtures in a system comprised of two porous materials: aerogel and silver sinter. The particle number density, and thus the ³He–⁴He concentration, was measured directly in the aerogel sample. We discuss both the observed history dependence for the low temperature equilibrium ⁴He fraction in aerogel and the temperature evolution of the ⁴He fraction.     

4He Impurities in 3He: Energetics and Dynamics

We have developed the optimized Fermi Hypernetted Chain Theory of a single impurity atom in a Fermi liquid, and have applied the theory to a ⁴He atom in bulk ³He. Previous applications of the theory for one component have produced excellent agreement with the experimental equation of state of ⁴He; the resulting equation of state of bulk ³He is about 0.4 K above the experimental one. Within the same theory, we obtain the pressure dependence of the chemical potential of ⁴He in bulk ⁴He, ³He in ³He, as well as the chemical potential of a ⁴He impurity in ³He. The pressure dependence of the impurity chemical potential agrees well with the experimental data, but we have a constant energy offset of about 1.2 K that disallows conclusive statements. This offset is partly explained by the relative inaccuracy of the ³He equation of state. We then calculate the self-energy of a single ⁴He impurity in ³He. Our results for the effective mass m^* ₄ fall within the experimental error of the best available data; they increase from about m^* ₄/m₄1.4 at zero pressure, to m^* ₄/m₄1.6 at p=20 atm. We show that this effective mass enhancement is, to about equal parts, due to hydrodynamic backflow and to the coupling to particle-hole excitations. When the latter are turned off in the collective approximation of the impurity-background correlations one obtains a significantly lower effective mass, m^* ₄/m₄1.2–1.35.     

Fast Pressure Quenches Near the λ- Line in 4He

The formation of topological defects during phase transitions was first discussed by Kibble¹ within a cosmological context. The idea was further developed by Zurek² for condensed matter systems, such as the λ-transition in ⁴He. The vortex density generated during a pressure quench through the transition is expected to be controlled by the quench rate, and can be determined from the attenuation of a second sound pulse. In previous experiments³ using mechanical means to generate the quench no vortex formation was observed. We increased the quench rate by four orders of magnitude using a hemispherical ugtrasonic transducer. No attenuation of second sound was observed, except for ambient conditions close to the λ-line and quench depth sufficient to also create cavitation.     

NMR Studies of 3He Droplets in Dilute 3He-4He Solid Solutions

We have performed measurements of the temperature dependence of the nuclear spin-lattice relaxation times (T ₁) for a wide range of ³He concentrations for dilute mixtures of ³He in solid ⁴He. The temperatures for phase separation are determined for ³He concentrations 500<x ₃<2000 ppm for a molar volume V _M =20.7 cm³. We report the temperature dependence of the nuclear spin-lattice relaxation times for ³He in the droplets formed after phase separation at low temperatures. The temperature dependence suggests that the interface ³He atoms responsible for the relaxation are degenerate, not solid-like.     

3He Transverse Excited State Occupation in Thin 3He-4He Films

The discovery that ³ He was occupying transverse excited states at submonolayer coverages in ³ He-⁴ He mixture films on a Nuclepore substrate, was a surprise. In this note we discuss the relationship between theory and experiment in attempting to understand the physics of this behavior. We first discuss various single-atom-limit calculations of the level spacing between the ground-state and first excited state. We then introduce a free, quasi-particle picture for analyzing experimental magnetization step data and compare those results with the single-atom-limit calculations. The experiments clearly show excited state occupation at submonolayer coverages in contradistinction with the calculations. We then briefly discuss a microscopic, semi-phenomenological theory which, in agreement with experiment, yields ³ He occupation of the first excited state at submonolayer coverages. The mechanism is a model ³ He-³ He effective interaction due to one ripplon exchange. This effective interaction is density dependent and very long ranged. It strongly modifies the small-k properties of the ³ He self-energy and, in particular, causes the ground-state to first excited state level spacing to decrease with increasing ³ He areal density.     

3He Spin Diffusion Measurements for 3He - 4He Mixture Films on Nuclepore

Preliminary ³ He spin diffusion results for ³ He - ⁴ He mixture films on Nuclepore are presented as a function of ³ He coverage for 0.1 T 0.3 K. We report measurements for a constant ⁴ He coverage of 4.41 bulk density atomic layers with ³ He coverages between 0.3 and 2.1 layers. The diffusion is observed to decrease with increasing amounts of ³ He, and some structure as a function of temperature is present.