Characterization of MEMS Devices for the Study of?Superfluid Helium Films

Measurements on the mechanical properties of MEMS resonators were performed to characterize such devices at room temperature and low temperatures. Using state-of-the-art silicon integrated circuit technology, we have designed, fabricated, and manufactured resonators consisting of a pair of parallel plates with a well-defined gap whose size can be controlled with a high accuracy down to the sub-micron range. A full study of resonance properties at various pressures was performed at room temperature. We will discuss the details of design, fabrication, and operation. These studies open up a window of opportunities to look for novel phenomena in quantum fluids such as in superfluid ³He films.     

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.     

Textures and Exotic Vortices in Neutral Fermion Superfluids

There has been intense interest in various Fermion superfluids in neutral atom liquids and gases, including chiral p-wave pairing in ³He-A phase and Feshbach-resonanced ⁶Li atom gases and d-wave pairing in atom gases. It is particularly interesting to find exotic vortices and associated low-lying Fermionic excitations under rotation. Here we report on our efforts of those topics: (1) Majorana Fermion in chiral superfluids near a p-wave Feshbach resonance. (2) Possible half-quantum vortices in p-wave superfluids of trapped Fermion atom gases. (3) Stability of a half-quantum vortex in rotating superfluid ³He-A between parallel plates. (4) Majorana bound state in rotating superfluid ³He-A between parallel plates. (5) Non-Abelian Fractional vortex in d-wave Feshbach resonance superfluids. We will summarize some of those works in a coherent manner in order to bridge the understanding between cold atom community and superfluid ³He community by stressing the importance of cross fertilization between them.     

Superfluid density of3He measured by fourth sound

Superfluid density of³He has been measured using fourth sound in two superleaks: “confined,” packed powder and “open,” parallel channels. The superleak pore size has little effect on the superfluid density near the melting pressure, but it has surprisingly large effects at lower pressures. The open, parallel channel superleak results show an unexpected pressure dependence of “strong coupling” effects and an unexpectedly small superfluid density change at the B→A transition.     

Unusual Behavior of a MEMS Resonator in Superfluid 4He

Novel mechanical resonators based on micro-electro-mechanical systems (MEMS) technology were developed for the study of superfluid ⁴He. The MEMS device is composed of two parallel plates, the movable plate suspended by four serpentine springs above the substrate, forming a shear mechanical oscillator. A specific device with a 1.25 μm gap was tested in the superfluid phase of ⁴He. At temperatures below 400 mK the device exhibits nonlinear and hysteretic behavior when the excitation exceeds a threshold. The anomalies are reminiscent of quantum turbulence and vorticity effects observed in other mechanical oscillators such as tuning forks or vibrating grids.     

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.     

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.     

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.      

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.     

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.      

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.     

Vibrating Wire Measurements in Superfluid 3He at the Melting Curve Down to 0.53 mK

Measurements of the vibrating wire spectrum have been carried out in superfluid ³ He along the melting curve down to 0.53mK. We have observed that at temperatures below 0.3 T_c the width of the mechanical resonance of the wire decreases exponentially with 1/T, indicating the ballistic regime of collisions with quasiparticles. The value of the superfluid energy gap was found to be (1.99±0.05)T_c, in good agreement with the values obtained from heat capacity measurements. The vibrating wire was thereby calibrated for further experiments at temperatures below 0.5mK, where the sensitivity of the melting curve thermometry becomes rather poor.     

On Third Sound Amplification by Stimulated Condensation

We describe the process by which condensing ⁴ He vapor atoms are expected to contribute coherently to the macroscopic superfluid motion of a third sound resonance. This phenomenon is similar to the experimentally observed thickening of a film in the fixed velocity state of a persistent current, though with an interesting and subtle difference. As before, the condensing atoms contribute to the kinetic energy of the macroscopic state by the coherent normal-to-superfluid conversion. In the present case, however, the macroscopic state is an oscillatory third sound mode. This allows the energy to remain in the third sound mode even if superfluid is removed by film flow in order to keep the film thickness constant. Thus, a continuous process of third sound amplification by stimulated condensation should accompany a condensing vapor flux under the right conditions.     

Nuclear magnetic resonance of3He superfluid confined in high porosity aerogel

We report pulsed nuclear magnetic resonance (NMR) measurements of the transverse frequency and magnetization of³ He confined in aerogel with 98.2% open volume porosity. A homogeneous superfluid phase is observed at pressures, P > 12 bar, accompanied by a sharp onset of frequency shifts showing little or no textural broadening; a result quite unexpected for³He confined in random porous media. The transition temperatures and order parameter are both significantly suppressed from their bulk values and the magnetization data indicate this low temperature phase is an equal-spin pairing superfluid. For NMR tipping angles greater than 40 ° the resonance frequency drops abruptly to the normal state value. This tip angle dependence is not consistent with either the bulk³He-A or³He-B superfluid phases.     

A Model for Third Sound Attenuation in Thick 4He Films

Third sound attenuation in thick ⁴He films has been observed to be much greater than predictions based on known mechanisms. We propose a possible mechanism for this observed high attenuation. Pinned vortices, possibly created when the superfluid transition is traversed, undergo driven oscillations in the third sound wave flow field. The dissipation is caused by two related effects. The first is due to the mutual friction between the vortex cores and the normal component. The second, larger contribution, is due to the drag experienced by a vortex-induced surface dimple. Variations in vortex density explain quite naturally the observed lack of reproducibility in attenuation measurements. A vortex density on the order of 10¹⁷m^–2 is required to account for dissipation reported in several experiments. We discuss the temperature, frequency and thickness dependence of the dissipation. The proposed model is also applicable to a vortex contribution to fourth sound attenuation. If third sound attenuation is indeed a signature of a very dense array of pinned vorticity, then our conception of a homogeneous superfluid film needs considerable alteration.     

Polarization Effects in Superfluid 4He

A theory of thermoelectric phenomena in superfluid ⁴He is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid ⁴He generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.     

More about Rotons in Superfluid Helium 4

In a recent paper¹ it was argued that rotons in superfluid helium 4 are the soft modes announcing a charge density wave that leads to the crystal: rotons are a normal state property. A small superfluid condensate acts to hybridize quasiparticles and soft density fluctuations - hence a level repulsion that lowers the energy: superfluidity is energetically favourable. A shallow roton implies a very small condensate density, as found in He4: what we need is a saturation mechanism. The clue is depletion due to quantum fluctuations. In (1) we assumed that such a depletion was drawn from the condensate itself: superfluidity then disappears in the liquid if the roton gap is too small. Here we explore an alternate possibility: quantum fluctuations are drawn from the normal fluid. We reach the opposite conclusion: superfluidity persists down to the spinodal limit where the roton gap vanishes, with an unusual power law dependence. We briefly mention the possible extension of that argument to a frozen charge density wave: in a toy 1d model it might shed light on the features that favour supersolids.     

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.     

Anisotropic second sound in superfluid 4He near T λ in the presence of a heat current

In the presence of a homogeneous heat current the isotropy of superfluid ⁴He is broken and the propagation of second-sound waves becomes anisotropic. We calculate the angular dependence of the velocity and damping of second sound near T within model F of Halperin, Hohenberg and Siggia to leading order in the renormalized couplings. The critical behavior is incorporated using results of the renormalization-group theory. Second-sound waves propagating parallel to the heat current become unstable if the heat current exceeds some critical value. The theory agrees with recent experiments.     

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.