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.      

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.     

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.     

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.     

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.     

Proximity Effect between a Dirty Fermi Liquid and Superfluid 3He

The proximity effect in superfluid ³He partly filled with high porosity aerogel is discussed. This system can be regarded as a dirty Fermi liquid/spin-triplet p-wave superfluid junction. Our attention is mainly paid to the case when the dirty layer is in the normal state owing to the impurity pair-breaking effect by the aerogel. We use the quasiclassical Green’s function to determine self-consistently the spatial variations of the p-wave order parameter and the impurity self-energy. On the basis of the fully self-consistent calculation, we analyze the spatial dependence of the pair function (anomalous Green’s function). The spin-triplet pair function has in general even-frequency odd-parity and odd-frequency even-parity components. We show that the admixture of the even- and odd-frequency pairs occurs near the aerogel/superfluid ³He-B interface. Among those Cooper pairs, only the odd-frequency s-wave pair can penetrate deep into the aerogel layer. As a result, the proximity-induced superfluidity in a thick aerogel layer is dominated by the Cooper pair with the odd-frequency s-wave symmetry. We also analyze the local density of states and show that it has a characteristic zero-energy peak reflecting the existence of the odd-frequency s-wave pair, in agreement with previous works using the Usadel equation.     

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.     

Magnetic Susceptibility of the Balian–Werthamer Phase of 3He in Aerogel

The equilibrium superfluid phase of ³He impregnated into high-porosity (98%) silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian–Werthamer (BW) phase modified by the depairing effects of the aerogel structure. The nuclear magnetic susceptibility played a key role in identifying the B-phase of pure ³He with the BW state. We report theoretical calculations of the nuclear magnetic susceptibility for the BW model of superfluid ³He in aerogel within the framework of the Fermi-liquid theory of superfluid ³He. Scattering of quasiparticles by the aerogel, in addition to Fermi-liquid exchange corrections, leads to substantial changes in the susceptibility of the BW phase. The increase in the magnetic susceptibility of ³He-aerogel compared to pure³He-B is related to the polarizability of the gapless excitations and the impurity-induced local field. The limited data that is available is in rough agreement with theoretical predictions. Future measurements could prove important for a more definitive identification of the ordered phase, as well as for refining the theoretical model for the effects of disorder and scattering on the properties of superfluid ³He.     

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.     

The Damping of a Quartz Tuning Fork in Superfluid 3He-B at Low Temperatures

We have measured the damping on a quartz tuning fork in the B-phase of superfluid ³He at low temperatures, below 0.3T _c. We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid ³He-B and in superfluid ⁴He at low temperatures. In superfluid ⁴He the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid ³He the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid ³He-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid ⁴He.     

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.     

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.      

Superfluid 3He in Presence of Spin-Polarized Scattering Centers

The influence of spin-exchange scattering centers on triplet Cooper pairing is considered by exploring the behavior of superfluid ³He in high porosity aerogel, containing ³He atoms localized on the surface of silica strands. The homogeneously distributed isotropic scattering system of spin-polarized impurity centers is adopted as a simple model to investigate the contribution of the spin-exchange scattering channel for quasiparticles to the formation of non-unitary superfluid A₁-phase in the aerogel environment. It is demonstrated that an interference between the potential and exchange parts of quasiparticle scattering from spin-polarized impurity centers can change considerably the temperature width and the spin structure of the A₁-phase in aerogel. PACS numbers: 05.70 Ln, 05.70 Jk, 64.     

Frictional Relaxation Time of 3He Normal Fluid Component in Aerogel Obtained by Fourth Sound Resonance

Recently, we revealed that the motion of the normal fluid component in the aerogel is well described by the frictional relaxation model (Higashitani et al. in Phys. Rev. B 71:134508, 2005). To clarify the origin of the friction between the quasiparitcles and the aerogel, we have performed the fourth sound resonance experiments at two different pressures. The fourth sound resonance experiment can derive both the static and the dynamic informations simultaneously, namely, the superfluid fraction and the energy loss. From the static part, we found that the superfluid fraction slightly changes with changing the pressure. We calculated the density of states in the impurity system by means of HSM and propose that the constituent of the normal fluid component is the quasiparticles at emerging levels in the energy gap, which we call the midgap states. From the dynamic part, we found that the energy loss depends on the pressure, in contrast to the superfluid fraction. The pressure dependence of the frictional relaxation time has been calculated, and we revealed that the response of the normal fluid component against the frictional force depends on the BCS coherence length.     

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.     

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     

Non-linear Mechanical Response of the A-like Phase of Superfluid 3He in Aerogel

We present measurements of the response of the A-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 low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.     

Quantitative Ratio of Heat Flows Due to Second Sound to Dissipation in Superfluid 3He-4He Mixtures

In this paper we compare two hydrodynamic modes in superfluid ³He-⁴He mixtures, focusing on which mode gives greater contribution to propagation of heat in superfluid liquids. Starting from the two-fluid hydrodynamic model, the quantitative contributions of second sound mode and dissipative thermal conductivity mode to the total heat flow are studied. The problem is considered in a cell with heat source of a form Q ₀cos²(ωt) at one side. Analytical expressions for space-time temperature and heat flow dependence are obtained and discussed.     

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.     

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.