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.     

Acoustic Resonance of Superfluid 3He in Parallel Plates

We performed an acoustic resonance experiment of superfluid ³He confined in a stack of parallel plates, and found the fourth sound resonance. From its velocity, the superfluid density fraction was calculated. No size effect was found because the gap between parallel plates were much larger than the superfluid coherence length. The energy loss of the resonance was also measured. We found that the hydrodynamic theory qualitatively described its temperature dependence, but it could not describe the gap width dependence. Possible explanations is discussed in the text. More over, we found the unidentified resonance that cannot be explained by conventional sound modes.     

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.     

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.     

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.      

Nuclear Spin Relaxation in Glass States of 3He-A in?Stretched Aerogel

We present results of pulse NMR investigations of superfluid A-like phase of ³He in stretched aerogel. In this case we have anisotropic orbital glass (OG) with two possible types of ordering in spin space??ordered spin nematic (OG-SN) or disordered spin glass (OG-SG) states. It was found that longitudinal relaxation of magnetization is non-exponential in both states and depends on temperature and on inhomogeneity of external steady magnetic field. At the same conditions the relaxation in OG-SG state is more rapid than in OG-SN state. For transverse orientation of the magnetic field relative to anisotropy axis the duration of free induction decay signal was longer than in normal phase. It may be explained by formation of coherently precessing spin state.     

Experimental studies on fourth sound in superfluid helium

In a superfluid liquid-helium cavity packed with a fine powder, only the supercomponent is free to move and pressure waves transmitted by the supercomponent are called fourth sound. We have observed that the resonance frequency of the powder-filled chamber may be shifted by introducing vortices. Both static and dynamic measurements were made on the resonance frequency and signal height in order to explore the effect of exceeding the critical velocity of the superfluid in the powder-filled chamber.Supported by the Robert A. Welch Foundation, Houston, Texas.     

Can Superfluid Vortex Lines Excite Normal Fluid Turbulence in 4He?

When helium II is made turbulent the superfluid component forms a dense tangle of quantized vortex lines which can be easily detected experimentally using the second sound technique. On the contrary little is known about the normal fluid component: on the experimental side progress has been hindered by the lack of simple flow visualization, and on the theoretical side attention has been concentrated on the effect that a given normal flow has on the superfluid vortices, not vice-versa. Attempting to fill this gap, we discuss results of recent calculations in which we find that normal fluid vorticity structures can be generated by superfluid vortices. In particular we address the issue of whether the superfluid vortices can make the normal fluid turbulent.     

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.     

Acoustic Modes and Momentum Relaxation in 2D Atomic Hydrogen on Helium Surface

Seeking for manifestations of superfluidity in 2D spin-aligned atomic hydrogen (H↓) adsorbed on the surface of liquid helium at T∼0.1 K we consider possible acoustic modes in this 2D Bose gas depending on frequency and on characteristic times of energy and momentum transfer. At high frequencies, the analogues of ordinary and second sound are realized in 2D H↓. At low frequencies, the 2D analogue of the fourth sound is realized: the normal component of hydrogen and ripplons are immobile and only the superfluid component of hydrogen participates the oscillations. We also estimate the rate of momentum relaxation between superfluid hydrogen and ripplons, τ _HR⁻¹ ∝ T ^13/3. The most promising for observing the superfluidity in 2DH↓ is the fourth sound, which could be excited, e.g., by ESR.     

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.     

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid ³He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid ³He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.      

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.      

Vortex Core Transitions in Superfluid 3He in Uniaxially Anisotropic Aerogel

Vortex core transitions (VCTs) in the superfluid phases of liquid ³He in uniaxially stretched and compressed aerogels are theoretically investigated. Uniaxial deformation imposed on the aerogel alters superfluid pairing symmetries in aerogels and the axial and polar pairing states are favored. In this study, we examine whether the effects of the uniaxial anisotropy on the pairing symmetries are reflected in core states of a single vortex extending along the deformation axis. By numerically solving the Ginzburg-Landau equations, we find that in the compressed aerogel, the first order VCT appears at any pressure in the B-like phase, while in the stretched aerogel, the VCT in the B-like phase is lost. Further, the vortices in the A-like phase in the stretched aerogel, have a polar core state in place of the A-phase core of the nonsingular Mermin-Ho vortex.     

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.     

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.     

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.     

Deep inelastic neutron scattering from liquid4He in aerogel glass

We report highQ inelastic neutron scattering studies of liquid⁴He confined inside porous aerogel glass in both the normal and superfluid phases. The scattering consists of a broad component, which we interpret as due to atoms localized on the surface of the glass, and a narrow component, which we interpret as due to the confined liquid inside the pores. The broad component is quite small, and no quantitative analysis is attempted. However, the narrow component due to the confined liquid is sufficiently large that information on the kinetic energy and condensate fraction may be obtained. The measurements are at large enoughQ (23 Å^–1) that the incoherent approximation may be used to directly extract the kinetic energy. Furthermore, the observed scattering is consistent with the impulse approximation, allowing information on both the momentum distribution and the condensate fraction to be extracted. The kinetic energy of the confined liquid is close to previous measurements of the kinetic energy in the bulk liquid. The condensate fraction of the confined liquid, which is estimated using a modification of a method due to Sears, is close to previous estimates of the condensate fraction in the bulk liquid.     

The Thermal Conductivity of Superfluid 3He in Aerogel: A Measurement of the Energy Gap

Transport properties of superfluid ³ He in aerogel are governed by a fixed mean free path set by the typical dimensions of the strand separation. We describe preliminary measurements of the thermal conductivity of superfluid ³ He confined in 98% silica aerogel. The majority of the measurements are made in relatively high magnetic fields where the superfluid within the aerogel is in the A-phase like state. Since the quasiparticle mean free path is fixed, the temperature dependence of the thermal conductivity depends only on the superfluid energy gap and on the texture in the case of the A-phase. The results so far obtained are broadly consistent with the aerogel-confined superfluid having a temperature dependent energy gap close to the BCS prediction although there are significant deviations at the lowest temperatures.     

Hydrodynamic theory of fourth sound in clamped conditions

The hydrodynamic theory of fourth sound is developed in detail for the cases of a flat capillary and a porous superleak filled with superfluid helium whose normal fluid motion is completely clamped. The attenuation is calculated including rigorously all the thermal conduction effects in both the helium and the capillary walls. Also included in the case of the superleak are the Rayleigh scattering and the thermal effects of the resonator walls. Comparison of the superleak results with existing experiments leads to the conclusion that Q factors of fourth-sound resonators could be increased considerably.