Sound Experiments on Superfluidity of 3He in Highly Porous Aerogels

We have carried out sound experiments on superfluid ³ He in three highly porous aerogels with different porosities. Two of the acoustic cells contain aerogels inside the pores in roughly sintered silver powder to avoid the vibration of the aerogel. In these acoustic cells we have detected fourth sound, and extracted the superfluid density from the fourth sound velocity. The effect of the sintered silver on superfluid ³ He was examined by using another acoustic cell which contains the sintered silver without aerogel. The size of the pores in the sintered silver was large enough not to show the size effect of superfluid ³ He and small enough to observe fourth sound of ³ He. In another cell without sintered silver, we have observed second-sound-like signal. The superfluid transition temperatures of ³ He are suppressed more in higher density aerogel. The aerogel density dependence of the suppression of the superfluid transition temperature of ³ He in aerogel can be explained qualitatively by the simple s-wave scattering approximation. However, the superfluid density shows quite different pressure-dependence in different porous aerogels. The reason of this phenomenon is not understood yet.     

Acoustical Experiments on Superfluid 3He-4He Mixtures in Aerogel

This report discusses our results on the superfluidity of ³ He- ⁴ He mixtures in a 98% porosity silica aerogel. We have used low frequency sound to probe helium mixtures confined to aerogel, and have observed both the slow mode of superfluid ³ He in aerogel, which is manifested only below T_c, and an additional sound mode present only in the mixture. We attribute this novel sound mode to the slow-mode in the ⁴ He rich phase of the dilute ³ He- ⁴ He mixture. This mode exhibits positive frequency shifts below T_c in aerogel, while above T_c the mode is observed at a temperature independent frequency until close to T where it shifts to zero frequency.     

Tortuosity and Dissipation of Liquid 4He in Aerogel

No Heading Flow of liquid ⁴He through silica aerogel has been studied by means of a torsional oscillator. Preliminary results on the tortuosity and dissipation of the ⁴He flow in 88%-porous aerogel are compared with earlier measurements on a 92%-porous sample where a transverse sound resonant technique was used. A hydrodynamic model for saturated superfluid helium in porous media is presented and its predictions are compared with the experimental results.PACS numbers: 67.40.HF, 67.40 Pm, 61.43.Gt     

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.     

Acoustic Spectroscopy of Superfluid 3He in Aerogel in the Presence of a Magnetic Field

We have constructed a silver alloy cell to investigate low frequency sound propagation in ³ He-filled aerogel at various magnetic fields. In this apparatus, two sound modes were observed in the superfluid phase. We observed both the first sound-like mode (fast mode) which is a compression wave also seen in the normal state and the second sound-like mode (slow mode) which is attributed to the out-of-phase oscillation of the superfluid and normal components of ³ He clamped to the aerogel matrix. The values of T_c and _s can be extracted from the analysis of these two modes. In addition, a Helmholtz resonance provides an in-situ signature of the bulk superfluid transition and allows us to also determine the bulk _s. By measuring these quantities over a range of applied magnetic fields we hope to explore the P, T, H phase diagram of ³ He in aerogel.     

3He-4He Mixtures in 95% Porous Aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures in 95% porous aerogel found a phase diagram similar to that in 98% porous aerogel. The coexistence boundary on the ³ He rich side resides very close to, but nevertheless is detached from the superfluid transition line. Together with the findings in 98%, 87%, and 99.5% porous aerogel, this result supports the interpretation that the phase separation of ³ He- ⁴ He mixture in aerogel is induced by the capillary condensation of ⁴ He films from neighboring silica strands into ⁴ He rich domains.     

NMR Study of Superfluid Phases of 3He Confined in 97.5% Porous Silica Aerogel

We have studied the scattering effect from aerogel strands on superfluid phases of ³He by a cw NMR method at 920 kHz. Liquid ³He at a pressure of 13 bar was confined in 97.5% porous aerogel from the same batch as that of a recent 4th sound study. The NMR experiment was performed in a magnetic field of 28.4 mT down to 0.3 mK. As temperature decreased, the NMR resonant frequency increased below 0.76 mK. The temperature of 0.76 mK agrees with the superfluid transition temperature T ^aerogel _c observed in the 4th sound study at the same pressure. Below T ^aerogel _c the behavior of thefrequency shift as a function of temperature indicates that there is no phasetransition to the other superfluid phase down to about 0.4 T ^aerogel _c . Owing to a very large surface solid ³He magnetization, we could not determine the superfluid phase of ³He in the aerogel in the magnetization measurement.     

Transverse Resonances in Aerogel with Liquid 4He

We present preliminary studies of transverse resonances in a thin disk of aerogel filled with normal and superfluid ⁴ He in the temperature range 1.4 to 3 K. We observed a broad temperature independent mode in the normal phase and three narrow critical modes in the superfluid phase. The system was modeled by combining the equations of superfluid hydrodynamics of helium with those of elasticity of aerogel. Analytical solutions were obtained for a resonator of square profile and two types of boundary conditions at the transducers/aerogel interface. Comparison of the model solutions with the experimental data showed that the dynamics of the oscillation was dominated by compression rather than shear as in pure transverse sound. Recommendations for future improvements are made.     

Crystallization of 4He in Aerogels

Static behaviors of crystallization of ⁴He in porous materials, such as the increase of melting pressure, have been studied extensively, but nonequilibrium dynamics of the phase transition is hardly known. Our interest was in how ⁴He crystals grow in a 90.4% porosity aerogel. Aerogels are transparent and the dynamics in them can be studied visually. A Pomeranchuk-type variable-volume cell was used to study crystallization at a fixed temperature with a blocked capillary condition. By continuously compressing a chamber, the pressure rose above the bulk melting pressure and at a pressure 1.7 bar above the bulk melting pressure these crystals began to invade the aerogel. A clear crystal-superfluid interface was moved smoothly by the steady compression. No macroscopic facets were observed in the aerogel well below the bulk roughening transition temperature.      

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of ³ He in different samples of silica aerogel. Several of these samples have been characterized using x-ray imaging, yielding information about the microstructure of the aerogel. In comparing new measurements on a 99.5% sample with previous observations on the behavior of ³ He in 98% porous aerogel we have found evidence for a scaling of the superfluid transition temperature to the correlation length of the aerogel. Furthermore, the superfluid density exhibits a similar universal behaviour over a range of values of reduced temperature. We discuss these new results in the context of superfluid pairing in the presence of a correlated disorder, specifically focussing on the fractal nature of the aerogel.     

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.     

Absence of Slow Sound Modes in Supersolid 4He

Torsional oscillator experiments on solid ⁴He have been interpreted as showing mass decoupling similar to what one observes in a superfluid. Within the context of a two-component model for the supersolid one would expect the appearance of a second, slow acoustic mode. We have searched for this mode using an acoustic resonance technique. We have used porous membranes in bulk solid ⁴He analogous to a second sound experiment in the superfluid. We also investigated solid helium in Vycor using piezoelectrically driven titanium diaphragms (analogous to a fourth sound experiment in the liquid). Our measurements have shown no indication of an additional sound mode in the kHz range.     

Transverse Sound in Helium Filled Aerogel

Transverse sound in superfluid ⁴He in 92% porous aerogel has been studied in a resonator with thin slab geometry, in the temperature range 0.6 to 2.8 K. The sound velocity and dissipation in the saturated aerogel were modelled using two fluid hydrodynamics, modified to account for the presence of the aerogel. Partially filled aerogel was also studied. Adsorption and desorption isotherms displayed hysteresis. For capillary-condensed films, the tortuosity and the dissipation scale with the amount of helium.     

Collision Drag Effect on Two-Fluid Hydrodynamics of Superfluid 3He in Aerogel

Sound propagation in superfluid ³He in aerogel is studied on the basis of a two-fluid model taking into account the effect by the drag force due to collisions between ³He-quasiparticles and aerogel molecules. The drag force plays a role of frictional force between the aerogel and the normal-fluid component. In local equilibrium, they move together in accordance with McKenna et al.'s model. The deviation from the local equilibrium leads to the damping of sound. We give explicit expressions for the attenuation of longitudinal sounds in this system. We also discuss the sound propagation in a superfluid ³He-aerogel system embedded in a narrow pore. It is shown that the fourth sound propagates in such a system because of the clamping of the normal fluid by the aerogel.     

Sound Modes of Superfluid 3He in Aerogel

We present the results of experiments on sound propagation at audio frequencies in ³ He-filled aerogel. Sound modes were observed at temperatures of 0.8–100 mK in an aerogel sample of 98% porosity. We find that below T _c for superfluid ³ He in the aerogel matrix the speed of sound in the composite system increases by as much as 1.5%. Also below the aerogel T _c new modes appear which correspond to propagation speeds of up to 10 m/s.     

Sound Spectroscopy of the Superfluid Phases of 3He in Aerogel in Zero Magnetic Field

Low-frequency sound is used to study phase transitions of ³He confined in 98% open aerogel. Superfluidity is manifested by the onset of the low frequency (slow) mode whose velocity (as a function of pressure and temperature) was used to map out the phase diagram of the B-phase and the metastable A-phase of ³He in aerogel. Analysis of the slow mode's evolution with temperature allows the development of the superfluid fraction in the A and B phases to be determined. The metastable A-phase and the equilibrium B-phase can co-exist in a properly prepared sample. Both the superfluid transition and the A→B transition exhibit a finite width of ～20–25 µK.     

Sound Propagation and Transport Properties of Liquid 3He in Aerogel

Superfluid ³ He confined in aerogel offers a unique chance to study the effects of a short mean free path on the properties of a well defined superfluid Fermi liquid with anisotropic pairing. Transport coefficients and collective excitations, e.g. longitudinal sound, are expected to react sensitively to a short mean free path and to offer the possibility for testing recently developed models for quasiparticle scattering at aerogel strands. Sound experiments, together with a theoretical analysis based on Fermi liquid theory for systems with short mean free paths, should give valuable insights into the interaction between superfluid ³ He and aerogel.     

Nucleation and Avalanche of 4He Crystals in Aerogel

Dynamical transition of ⁴He crystals in aerogel was reported recently (Nomura et al. Phys. Rev. Lett. 101:175703, 2008). Bare aerogel, which was placed in the bulk ⁴He crystals, was used in the report. ⁴He crystals inside the aerogel grew via creep at high temperatures and via avalanche at low temperatures owing to the competition between thermal fluctuation and quenched disorder. Crystal-liquid interface advanced from the edge to inside of the aerogel. Crystal has a greater density than liquid so that the extra mass has to be transported in the crystallization process. It is not known how the mass is transported in the aerogel. To find a clue to this issue, we did an experiment with aerogel in a glass tube so that the aerogel had contact with the bulk on only one surface. In this case, a similar dynamical transition was observed at low temperatures. In the avalanche region, however, ⁴He crystals did not grow from the outer surface of the aerogel but nucleated at various sites inside the aerogel. This means that crystallization in aerogel does not occur by the forced invasion of ⁴He crystal but by a process of the bulk crystal once being melted and transported to increase the pressure of the liquid in the aerogel. Thus, a mass transport mechanisms for the crystallization has been revealed by this observation.     

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.     

Acoustics of a “Dirty” Fermi Liquid: 3He in Aerogel

An acoustic cavity containing ³He in 98% porous silica aerogel was used to investigate the effects of impurity scattering in a Fermi liquid. The pressure and temperature dependence of the sound attenuation in the normal Fermi liquid was extracted from the cavity response. The attenuation of sound displays behavior very different from the bulk owing to strong elastic scattering of quasi-particles by the silica strands. Using a visco-elastic model of the Fermi liquid, we find a mean free path restricted to 340 nm. Information on the sound velocity is inferred from the pressure dependence of the oscillation period of the cavity response. The data can be accounted for by a Biot model of the ³He liquid in the porous aerogel.