Energy Loss of Fourth Sound in Superfluid 3He within Small Pores

We performed a high-sensitivity fourth sound resonance experiment for pure superfluid ³He at 29.0 bar in sintered silver powder cell to clarify the hydrodynamic property of ³He in the aerogel-sintered silver system. We discuss the energy loss of fourth sound. An anomaly in the energy loss at the AB phase transition as found in the aerogel system was not observed. Our analysis shows that the energy loss Q ⁻¹, which monotonically decreases with decreasing temperature, can be understood by the hydrodynamic theory in the B phase qualitatively and quantitatively. We estimated the effective pore radius R in the powder cell.      

Fourth Sound Measurement of Superfluid 3He in Aerogel

The fourth sound resonance experiment has been done on liquid ³He in 98.5% porosity aerogel. Aerogel was grown inside the pores among the sintered silver powder to avoid the vibration of the aerogel strands by the sound experiment. The measurement was performed at zero magnetic field and 27 bar. We observed the phase transition between the A-like and B-like phases and also their coexistent state. The A-like to B-like phase transition occurs not at a temperature but within a temperature band. In this band, the A-like phase gradually converts to the B-like phase. Possible picture of the coexistent state is discussed.     

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.     

The Tricritical Region for Helium Mixtures in 0.87 Porosity Aerogel

We have used ultrasonic velocity measurements to study ³ He- ⁴ He mixtures in aerogel with a porosity 0.87. The phase diagram resembles that of bulk mixtures, with a single transition for ³ He-rich mixtures, in contrast to the detached phase separation curve seen in 0.98 porosity aerogel. A kink in the lambda line at a 3He concentration of X _C =0.51 suggests that the phase separation line meets it at a tricritical point. We have measured the amount of superfluid which decouples both at low temperature and close to the superfluid transition, as functions of ³ He concentration. Each showed a sudden change at the concentration where the kink appeared in the lambda line, suggesting an abrupt change in the morphology of the superfluid phase in the mixtures. Similar measurements were made for pure 4He films on the same aerogel. We discuss the nature of ³ He-rich mixtures in aerogels based on these experiments.     

Fast Mode in Dense Aerogel Filled with Superfluid He II and Dilute Mixture of 3He in 4He

Longitudinal sound wave propagation in 90% porous silica aerogel filled with superfluid He II and dilute mixture of ³He in ⁴He has been studied using a low frequency resonance method. The observed fast mode was identified as a mode intermediate between the sound in the aerogel matrix and first sound. It was shown that the behavior of the fast mode in dense aerogel differs from both high porosity aerogel and rigid porous medium. We discuss the obtained results within the framework of theoretical models available.      

Impurity Scattering Effect on Superfluidity of 3He in Aerogel

The impurity scattering effect on superfluid ³ He in aerogel is studied on the basis of the standard impurity theory within the weak coupling limit. We discuss the superfluid transition temperature and the superfluid density in the dirty Fermi liquid. The results are compared with recent experiments on the superfluidity of ³ He in aerogel. The low pressure data of the observed superfluid density are shown to be in better agreement with the results for the A-phase than for the B-phase. The B-phase results show considerable disagreement with the low pressure data.     

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.     

3He-4He mixtures in aerogel

Superfluid density and heat capacity experiments on³He-⁴He mixtures in 98% porous aerogel show that in this system the coexistence boundary is detached from the superfluid transition line. The tricritical point is removed, and there is a superfluid phase on the³He rich side of the phase diagram. The presence of heat capacity peaks along the transition line down to a⁴He concentration of only 8% indicates the 3-dimensional nature of this transition.This work is supported by NSF under grants DMR-9008461 and DMR-9311918.     

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.     

Superflow and dissipation in porous glasses

The study of superflow of ⁴ He in proous vycor glass has a long venerable history, dating back to the early days of superfluidity. In this work we wish to address a number of outstanding questions. In doing so we have used a low frequency (250 Hz) Helmoholtz oscillator technique which uses filled pores and allows measurements to be made on small samples under a variable pressure gradient and at any temperature - not only below the superfluid transition (a feature also of torsional oscillator ¹ and acoustic techniques². An introduction to the resonator has already been published ³ . The techique has also been used to investigate aerogel porous glass ¹¹ but the main emphasis of this report will be on vycor.     

Effect of Strong Magnetic Fields on Superfluid 3He in 98% Porosity Aerogel

No Heading We report our results of shear acoustic impedance measurements performed on superfluid ³He in 98% porosity silica aerogel. Experiments in high porosity aerogel provide unique opportunity to study the influence of disorder on a p-wave superfluid and compare the behavior with that of the well understood pure bulk. Our experiment is designed to detect acoustic signatures from both bulk liquid and liquid in aerogel. In the past, experiments on ³He in aerogel have been conducted in zero or low magnetic fields (< 1 tesla). We made measurements in magnetic fields as high as 15 tesla at 28.4 and 33.5 bars and observed a new phase in aerogel induced by magnetic fields splitting the superfluid transition into two.PACS numbers: 67.57Pq, 67.80Mg     

The superfluid fraction of3He confined in pores of sintered silver

We have measured the superfluid fraction of³He confined within the pores of silver sinter. Four sintered substrates were prepared with packing fractions between 23% and 68% of solid density. Measurements were carried out at six pressures between 0 bar and 29 bar. These results show that the superfluid fraction is suppressed to a much greater extent than expected.     

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.     

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.     

A Preliminary Heat Capacity Measurement of 3He in Aerogel near its Superfluid Transition

We report simultaneous heat capacity and torsional oscillator measurement of ³ He in aerogel near the superfluid transition. The heat capacity has a peak at the temperature T_c where the torsional oscillator shows the onset of superfluid decoupling. The coincidence of these signatures suggests that ³ He in aerogel does undergo a true thermodynamic transition.     

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.     

Possible Sound Mode Conversion in “Superfluid 4He-97% Open Aerogel” System

We have studied the acoustic properties of liquid helium filled in various aerogels. The longitudinal ultrasound velocity and attenuation were measured at the frequency of 10 MHz with aerogels that had porosity from 92 to 97%. The mode intermediate between first and fourth sound was observed. The attenuation of this mode decreased with decreasing temperature for dense aerogels. However, an attenuation maximum was observed around 1.6 K for 97% open aerogel at various liquid pressures. In the present work, we discuss the possibility of the sound modes conversion between first, second sound in superfluid and aerogel sound mode in this composite system.     

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 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.