Preliminary Measurements on Grid Turbulence in Liquid 4He

A grid has been pulled through a column of liquid helium at speeds as high as 1 m/s and at temperatures as low as 90 mK. A 300 micrometer Ge thermometer with response time of less than 1 ms measured the temperature rise resulting from the decay of the turbulence generated. It is believed that homogeneous, isotropic quantum turbulence was formed, since mesh Reynolds numbers in excess of 100,000 were created. The rates and power spectra of the energy increases detected in the helium after grid-pulls are determined. The results are compared to other quantum and classical results, and to the theory of the Kelvin wave cascade in a viscosity-free fluid.      

Scaling Results for Superfluid 3He in 98% Open Aerogel

We present experimental observations of the suppressed superfluid transition temperature, T _ca , superfluid fraction, ρ _s /ρ and Leggett frequency of ³He-B in aerogel, Ω _Ba . We determine T _ca from mass decoupling and the vanishing of the frequency shift away from the Larmor frequency in our different samples and different laboratories. We find that the suppressed transition temperature for ³He in aerogel occurs at a sample dependent, but approximately pressure independent, length, , where T _c and ξ ₀(P), are the transition temperature and the pressure dependent zero temperature coherence length for bulk ³He. T _ca also occurs at a pressure independent value of the Leggett frequency of bulk ³He-B. Further, we find that when the superfluid fraction and square of the Leggett frequency are plotted against T _ca −T (and not (T _ca −T)/T _ca ), the results of each measurement nearly collapse on to a pressure independent but sample dependent plot, with no further scaling. When plotted on a log–log scale, both measurements exhibit power laws in the range 1.33–1.45.      

Torsional Oscillator Measurements of Liquid 4He Confined in 2.2-nm Channels of FSM

We have performed torsional oscillator measurements for liquid ⁴He confined in 2.2-nm channels of FSM up to 2.45 MPa. At 0.1 MPa, the resonant frequency increases with decreasing temperature. It shows a small bend at about 0.9 K, and then keeps increasing down to the lowest temperature, 0.16 K. The magnitude of the frequency increase below 0.9 K is suppressed with increasing pressure, while the temperature of the bend shows almost no pressure dependence.      

Development of a low-temperature He compressor for superfluid He-He mixtures

The development, testing and modeling of a “compressor” that is capable of increasing the concentration of the ³He component of a liquid superfluid ³He-⁴He mixture is discussed. This compressor was developed to drive refrigeration cycles for cooling below 1 K. The compressor design and performance testing is described in detail. The compressor was operated at 1.2 K and ³He molar flow rates of 130 μmol/s were achieved. Compression ratios in excess of 6 were also demonstrated. The theoretical models presented are used to estimate the expected efficiencies of the compressor as well as the effect of the ⁴He component on the power required to drive the compressor.     

Bose-Einstein Condensation of Magnons in Superfluid 3He

The possibility of Bose-Einstein condensation of excitations has been discussed for a long time. The phenomenon of the phase-coherent precession of magnetization in superfluid ³He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different states of coherent precession has been observed in ³He-B: homogeneously precessing domain (HPD); persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and a mode of the coherent precession in compressed aerogel. The coherent precession has been also found in ³He-A in compressed aerogel. Here we demonstrate that all these cases are examples of a Bose-Einstein condensation of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by different types of spin-orbit coupling in the background of the coherent precession.      

Long-Range Order in the A-like Phase of Superfluid 3He in Aerogel

A mutual action of the random anisotropy brought in the superfluid ³He by aerogel and of the global anisotropy caused by its deformation is considered. Strong global anisotropy tends to suppress fluctuations of orientation of the order parameter and stabilizes ABM order parameter. In a limit of vanishing anisotropy fluctuations of ABM order parameter became critical. It is argued that still in a region of small fluctuations the order parameter changes its form to be less sensitive to the random anisotropy. For a favorable landscape of the free energy of superfluid ³He the fluctuations remain small even in a limit of vanishing global anisotropy and the long-range order is maintained.      

A-B Phase Conversion and Coexistence of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He at 2.4 MPa in cylindrical aerogel by NMR method. When the liquid is cooled down from the normal state, the A-like phase appears below superfluid transition temperature T _c ^a which is suppressed in comparison with the transition temperature of the bulk liquid. With further cooling below the certain temperature T _ab,c ^a , the A-like phase is converted into the B-like phase gradually. Both phases stably coexist within about 90 μK. When you keep the temperature constant in which both phases coexist, the A-B phase conversion stops. With furthermore cooling, the whole liquid becomes the B-like phase. The cwNMR spectra at the coexistence state suggest that the B-like phase is not uniformly distributed in the A-like phase like a large number of small bubbles in a liquid, but separated as a whole from the A-like phase. By applying a field gradient which changes as a function of square of radius, we found that the A-like phase is in the edge part with a cylindrical shape and the B-like phase is in the central part with a columnar shape.      

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.      

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.      

Instability of the Solid-Liquid Interface of 4He during a Large Transformation

We report an instability of ⁴He crystal surface during a large modification of its shape observed by schlieren photography. ⁴He crystal was nucleated on an ultrasound transducer which was placed in the upper part of the sample cell facing the bottom. The crystal was grown on the transducer and the lowest part of it eventually touched the bottom of the cell. Almost immediately, the crystal started to change shape very quickly to adjust itself to the new boundary condition. During this large deformation, the hexagonal shape of the crystal surrounded by facets became unstable and the surface became corrugated. The corrugation pattern during the deformation was observed by a high-speed camera. The results were compared with Kelvin-Helmholtz type instability which Uwaha and Nozières predicted.      

Large Boundary Magnetism and Superfluidity of Liquid 3He in Nanometer-sized Porous Alumina

Continuous-wave NMR measurements were performed for liquid ³He in porous alumina with nominal pore size of 20 nm in diameter, at temperatures down to 0.3 mK. The signal is composed of two contributions: from the liquid and from the boundary solid layer of ³He on the alumina’s surface. The latter shows a well-known ferromagnetic tendency and signal intensities can be fitted to a Curie-Weiss law in the high temperature region. The obtained Weiss temperatures are 0.18 and 0.50 mK at 7.5 and 28 bar, respectively. ⁴He coverage (4 monolayers) completely eliminates boundary signal between 7.5 bar and 32.5 bar. The residual liquid signal shows frequency shift and broadening below superfluid transition temperatures depending on liquid pressures. The obtained P-T phase diagram well resembles that of bulk liquid ³He in spite of the very narrow pore-size comparable to the coherence length of superfluid ³He.      

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.      

Model Calculation of Orientational Effect of Deformed Aerogel on the Order Parameter of Superfluid 3He

Theory of Rainer and Vuorio of small objects in superfluid ³He is applied for calculation of the average orientational effect of a deformed aerogel on the order parameter of ³He. The minimum deformation which stabilizes the ordered state is evaluated both for specular and diffusive scattering of quasiparticles by the strands of aerogel.      

Tricritical Dynamics at the Demixing-λ-Transition in 3He-4He Mixtures

We calculate in two loop order the dynamical critical behavior at the tricritical point occuring in ³He-⁴He mixtures. Model F^′ introduced by Siggia and Nelson (Phys. Rev. B 15:1427, [1977])—already problematic in one loop order—is shown in two loop order to lead to a divergence of the mass diffusion D in contradiction to experiments. Within the complex symmetric version of this model (model E ^⋆′) the dynamical critical exponents of the kinetic coefficients can be calculated exactly leading to a mass diffusion going to zero at the tricritical point as D(t _X )∼t _X ^1/2 (t _X is the relative temperature distance at constant concentration) and the thermal diffusion ratio k _T ∼t _X ⁻¹ diverges proportional to the concentration susceptibility in the experimental region. We also discuss effective dynamical critical exponents and compare them with recent simulations of the vector Blume-Emery-Griffths model.      

On the Correlation between Properties of Multielectron Dimples and Bubbles

Characteristics of multielectron dimples on the surface of liquid helium and those of multielectron bubbles arising in its bulk when the charged surface develops electrohydrodynamic instability are strongly interrelated. This circumstance allows one to explain a number of observable properties of multielectron bubbles in helium.      

Quartz Tuning Fork in Helium

Use of a quartz tuning fork for precise measurements of density has been studied in normal ³He liquid and in ⁴He liquid and vapor, spanning a reasonably wide range of fluid densities. It is evident that the compressibility of the fluid must be accounted for in order to properly interpret the resonator response.      

Quantum Fluid Dynamics of Rotating Superfluid 3He in Aerogel

Superfluid ³He A-like and B-like phases in 98% aerogel have been studied under rotation up to 2π rad/s by using cw-NMR and Homogeneous Pressing Domain (HPD) NMR at 29 mT and 3.0 MPa. Triplet superfluid ³He has continuous symmetries whose degeneracies are lifted by small perturbations of magnetic field, boundary condition of the sample cell, counterflow and global anisotropies of aerogel. We report NMR results of the two typical samples in aerogel under rotation, which are almost identical in the phase diagram, T _c and the critical velocity of the multiplication of vortex but are very different in textures and responses to the flow with each other. One samples (S-D) is slightly compressed by squeezing and thermal stress and thus has global anisotropic deformation along the sample axis. The other cell (S-H) has randomly(not uniaxially)-oriented global anisotropy. In the S-D, we observed a large negative shift in cw-NMR and spin wave and HPD in the B-like phase. Comparing textures determined by NMR and its response to the counterflows between two samples, we discuss how the long-range order of the continuous symmetry and textures are controlled by orientation effects due to global anisotropy in aerogel.      

Instability of Quantized Vortices Attached to Oscillating Boundaries in Superfluid 4He

The motion of quantized vortices is studied using a vibrating wire in superfluid ⁴He. A vortex filtering method provides a superfluid practically free of remanent vortices in which the vibration of a wire cannot generate turbulence. Vortex lines are produced by cooling through the superfluid transition and remain forming bridges between a wire and a surrounding wall. Bridged remanent vortices increase the resonance frequency of a vibrating wire: the rate of an increase due to the remanent vortices is constant in a laminar flow regime and steeply increases in a turbulent flow regime with increasing wire velocity. These results suggest that oscillation of the bridged vortices provides a linear contribution to the wire vibration in the laminar flow regime, until instability occurs in the oscillation of the vortices, causing turbulence.      

Simulations of Vortex Evolution and Phase Slip in Oscillatory Potential Flow of the Superfluid Component of 4He Through an Aperture

The evolution of semicircular quantum vortex loops in oscillating potential flow emerging from an aperture is simulated in some highly symmetrical cases. As the frequency of potential flow oscillation increases, vortex loops that are evolving so as eventually to cross all of the streamlines of potential flow are drawn back toward the aperture when the flow reverses. As a result, the escape size of the vortex loops, and hence the net energy transferred from potential flow to vortex flow in such 2π phase-slip events, decreases as the oscillation frequency increases. Above some aperture-dependent and flow-dependent threshold frequency, vortex loops are drawn back into the aperture. Simulations are performed using both radial potential flow and oblate-spheroidal potential flow.     

Neutron Diffraction Study of He Solidified in a Mesoporous Glass

He embedded in a porous glass has been studied by neutron diffraction. Along the isochoric path studied, about 30% of the pore filling solidify in the bcc structure at 1.7 K and remain in this state down to 60 mK, the minimum temperature of the experiment. The other part of the pore filling is either liquid or an amorphous solid. The behaviour is discussed in terms of a thermodynamic model.