Acoustic Resonances in Helium Fluids Excited by?Quartz Tuning Forks

Ordinary quartz tuning fork resonators, operated at about 30 or 200 kHz frequency, couple to acoustic first and second sound resonances in helium fluids under certain conditions. We have studied acoustic resonances in supercritical ⁴He, normal and superfluid ⁴He, and in isotopic mixtures of helium. Suggestive temperature, pressure, and concentration dependences are given. Furthermore, we propose a thermometric reference point device based on second sound resonances in helium mixtures, and indicate possible differences in the nature of second sound resonances in superfluid ⁴He and helium mixtures.     

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.     

A waveguide partially packed with superleak as a probe of superfluid properties

A waveguide partially packed with superleak and filled with superfluid ⁴ He is proposed as a useful configuration for studying acoustic modes. A calculation is performed indicating that the low-frequency propagating modes in such a system are of two types: a combined first/fourth sound mode and a modified second sound type mode. Experimentally, the waveguide is closed back on itself to form a toroidal resonator. Resonant frequencies were measured, and the experimental results compared favorably with the calculations. However, there remain unresolved discrepancies. This resonator may prove useful in measuring the possible superfluid properties of the new state of ³ He.     

Turbulence of Second Sound Waves in Superfluid 4He: Effect of Low-Frequency Resonant Perturbations

We report the results of investigations of acoustic turbulence in a system of nonlinear second sound waves in a high-quality resonator filled with superfluid ⁴He. It was observed that subharmonics of a periodic driving force applied to the system may be generated via a parametric instability. We find that application of an additional low-frequency pumping to the turbulent system results in the generation of waves at combination frequencies of the driving forces and also leads to substantial changes in the energy spectrum of the acoustic oscillations.      

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.     

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.      

Zeeman Splitting and Nonlinear Field-Dependence in Superfluid 3He

We have studied the acoustic Faraday effect in superfluid ³He up to significantly larger magnetic fields than in previous experiments achieving rotations of the polarization of transverse sound as large as 1710°. We report nonlinear field effects, and use the linear results to determine the Zeeman splitting of the imaginary squashing mode (ISQ) frequency in ³He-B.     

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.     

The transverse acoustic response of superfluid3He-B

For both normal and superfluid³He, the propagation of a collisionless transverse sound mode is predicted. The study of this mode in the normal fluid has been problematic: it travels only slightly faster than the Fermi velocity and is very highly attenuated. Early theoretical results suggested that transverse sound would not propagate in the superfluid and the experimental study of this mode was not actively pursued. However, recent theoretical work has predicted that this mode should indeed propagate, at sufficiently high frequencies and low temperatures, due to the interaction with the imaginary squashing mode. We present here an extensive experimental study of the transverse acoustic response in the B phase of superfluid³He. These measurements were performed on a short path length (30.5 microns) acoustic cavity, using a continuous wave, single ended, acoustic impedance technique. Simultaneous measurements were made of the longitudinal acoustic response, on an adjacent acoustic cavity of similar geometry. Both sound modes were excited at a frequency of 61 MHz. With this arrangement, well understood features in the longitudinal acoustic response were used as fiducial points for the study of heretofore ambiguous or unobserved features in the transverse acoustic response. As predicted by recent theoretical calculations, the transverse acoustic response was markedly different when the sound frequency was greater than the imaginary squashing mode frequency, as compared to when the sound frequency was less than the imaginary squashing mode frequency. At lower pressures the transverse acoustic response clearly exhibited the signatures of an evolving standing wave pattern (with the transverse sound velocity much less than the longitudinal sound velocity), and as such provides convincing evidence of a propagating transverse mode.     

Pressure release superleak sound modes in He II

The sound modes of He II in a waveguide partially packed with superleak are investigated for the case of a free surface within the waveguide. In the limit of zero vapor density, two propagating modes are found: one a gravity wave whose velocity depends on the superfluid fraction, and the other a temperature wave which is analogous to adiabatic U-tube osculations. With finite vapor the U-tube mode in pure ⁴He mixes strongly with the vapor sound; however, in ³He-⁴He mixtures it is uncoupled from the vapor and is observable. Experimental results are in qualitative agreement with the theory.Alfred P. Sloan Research Fellow.Project supported in part by NSF Contract DMR 76-22306, by ONR Contract N00014-75-C- 0246, and by the Research Corporation.     

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.     

Acoustic Emission by Quartz Tuning Forks and Other Oscillating Structures in Cryogenic 4He Fluids

We report on experimental investigations of acoustic emission by quartz tuning forks resonating at frequencies 32 kHz, 38 kHz, 77 kHz and 100 kHz immersed in cold gaseous ⁴He and its normal and superfluid liquid phases. Frequency dependence of the observed low-drive-linewidth at 350 mK together with the temperature and pressure dependences (1.3 K < T < 4.2 K, 0 < p < 25 bar) of the observed damping of the high frequency (77 and 100 kHz) resonators measured in normal liquid ⁴He and its superfluid phase provide strong and direct evidence of the importance of sound emission by these tuning forks. Three analytical models of acoustic emission by vibrating tuning forks are developed and compared with the experimental results. We also discuss the importance of sound emission for experiments with the commonly used 32 kHz tuning forks as well as other oscillating structures??spheres, wires, grids and various micromachined sensors. We compare the relative importance of dissipative losses due to laminar viscous/ballistic drag and acoustic emission in liquid and superfluid ⁴He.     

Imaginary Squashing Mode Spectroscopy of Helium Three B

We have made precision measurements of the frequency of a collective mode of the superfluid ³He–B order parameter, the J=2⁻ imaginary squashing mode. Measurements were performed at multiple pressures using interference of transverse sound in an acoustic cavity. Transverse waves propagate in the vicinity of this order parameter mode owing to off-resonant coupling. At the crossing of the sound mode and the order parameter mode, the sound wave is strongly attenuated. We use both velocity and attenuation measurements to determine precise values of the mode frequency with a resolution between 0.1% and 0.25%.     

Attenuation of superfluid two-phase sound

The attenuation of superfluid two-phase sound in⁴He is calculated and compared with experimental results. The dispersion relation of this mode (which consists of coupled vapor sound and second sound) is determined by boundary conditions at the free liquid surface. The primary source of attenuation is found to be the evaporation-condensation process at the free surface. A calculation using kinetic models for the nonequilibrium Onsager coefficients yields an attenuation in general agreement with experimental measurements.     

Supersolidity and Superfluidity of Grain Boundaries

We have looked for dc mass transport through solid ⁴He in a simple experiment with two communicating vessels filled with solid ⁴He in equilibrium with liquid ⁴He. Through good quality crystals, we have observed no mass transport, in contradiction with the hypothesis of a Bose–Einstein condensation of vacancies. Through crystals containing grain boundaries, we have found superfluid flow along these grain boundaries. We discuss these results in the context of other experiments on supersolidity.     

Melting of Solid 4He by Ultrasound at 1.2 K

We observed the melting of solid ⁴ He in superfluid when the sound waves were injected to its rough surface at 1.2 K. Single crystal was grown between two transducers and ultrasound pulses were applied normally to the solid-liquid interface from solid side or liquid side. Amount of melting was on the same order in both cases. We developed surface height measurement system using the sound wave itself and measured the amount of melting by changing the sound power and the number of pulses.     

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.     

Second Sound Horizon

We study an analogy between black hole physics and the phase boundary between normal and superfluid liquid helium in a gravitational field or in the presence of a constant heat current. We investigate the propagation of second sound near the boundary between superfluid and normal fluid. The speed of second sound should approach zero as it propagates toward the phase boundary where the reflection and transmission of the second sound will become ambiguous. This is analogous to the propagation of light near a singular black hole. When the phase boundary moves it is analogous to a black hole horizon: a second sound horizon. The analogy may lead us to infer a thermal radiation noise of amplitude <50 pico Kelvin from the boundary between the super and normal fluid. This thermal noise may be dramatize by applying a constant heat current from the bottom. We find a scaling behavior TQ ^1/6 for the thermal radiation of the phase boundary as a function of heat current Q. A feasible experiment to measure this thermal noise is suggested.     

Al/Au Bilayer Thermometer for Third Sound Detection

We present results from an experiment to develop bilayer metallic films of Al and Au as superconducting transition edge thermometers for the detection of third sound waves in thin superfluid ⁴He films. We compare transition edge data for such an Al/Au thermometer to that for a pure Zn thermometer and document its utility for third sound detection.     

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.