Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

Fermi liquid behaviour of the viscosity of3He-4He mixtures

We have investigated³He-⁴He mixtures at³He-concentrations 0.98%x9.5% by the vibrating wire technique in the temperature range 1 mKT 100 mK and at pressures 0 bar p 20 bar. In the degenerate regime of the mixtures the Landau theory of Fermi liquids predicts a temperature dependence of the viscosity proportionalT ^–2. We report on the first observation of this behaviour at 3 mKT 10 mK for all investigated concentrations and pressures. At temperatures below about 20 mK slip corrections had to be taken into account due to the increase of the quasiparticle mean free path at very low temperatures. The low-temperature cut-off in T ² = constant indicates the transition into the ballistic regime of the mixtures, where the mean free path of the quasiparticles exceeds the radius of the vibrating wire. Our results for the pressure dependence of the viscosity as well as for its magnitude show substantial differences from predictions based on pseudopotential theory. However, a calculation of with the quasiparticle interaction potential of recent solubility measurements in mixtures agrees well with our experimental data, in particular the pressure independence of .     

Nonlinear acoustic properties of vibrating wires at very low temperatures

We have investigated the acoustic properties of superconducting NbTi and Ta wires in vacuum at 1 mKT1 K and at a few kHz. The temperature dependence of the acoustic properties of the wires is similar to that found in amorphous materials: a maximum in the sound velocity and a plateau in the dissipation at temperatures above it. In addition, we have observed a strong influence of the acoustic power on the measured properties in agreement with recent measurements on amorphous SiO ₂ . This strain dependence can be interpreted by a modification of the tunneling model as a change of populationS of the two-level system energy states in non-crystalline materials. We can explain the strain-dependent anomalies as the superposition of three nonlinear effects: the change of population of the tunneling systems energy states, self-heating of the wire, and a nonlinear restoring force. These effects have a strong influence on the lineshape of the resonance curve. In addition, we have investigated the behavior of vibrating wires in liquid ³ He and liquid ³ He- ⁴ He solutions atT<100 mK. We can show that in superfluid ³ He-B atT<0.2 mK or in solutions of ³ He in ⁴ He with a small concentration of ³ He it is impossible to use a vibrating wire as a viscometer without having exact information about its intrinsic properties.     

Heat release,refrigeration and thermometry in3He-4He solutions at very low temperatures

We report on our measurements performed in liquid³He-⁴He solutions in the microkelvin temperature range at the Bayreuth nuclear demagnetization cryostat. One aspect of our work is the application of the vibrating wire technique for thermometry in the ballistic regime of phase-separated solutions. The establishment of reliable thermometry along with the particular design of our experimental cells enables us to study two main limitations on the minimum temperature of about 100K achieved in³He-⁴He solutions so far: the thermal resistance between the liquid and the cell, and the origins of the heat leaks.     

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in superfluid ³ He at ultralow temperatures. The aerogel dik is attached to a goal post shaped vibrating wire resonator and immersed in liquid ³ He cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below <0.11T_c. At higher pressures we observe large temperature dependent frequency shifts, reminiscent of torsional oscillator experiments. We find the transition temperature at 5 bar to be around 600K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of ³ He in aerogel in the ultralow temperature regime.     

Mean free path effects in superfluid4He

The mean free path effects in superfluid He II was studied with a vibrating wire method in the temperature range from T down to 20 mK under the saturated vapour pressure. The transition from the hydrodynamic regime to the ballistic regime was clearly observed at around 0.7 K with a 47 µm diameter wire. In the hydrodynamic regime the usual Stokes' approximation was found to be insufficient to interpret the results. In the ballistic regime the results can be explained quantitatively with the kinetic theory of phonons. However, below about 0.15 K there appear non-linear effects such as the distortion of the resonance line shape and a hysteresis behavior, which become stronger with decreasing temperature.     

The specific heat capacity and thermal conductivity of normal liquid3He

By observing the diffusion of a heat pulse along a 10-cm column of normal liquid³He with the aid of two vibrating wire thermometers, it has been possible to measure the heat capacityC and thermal conductivityK of the liquid in the temperature range fromT _C to 10 mK and at pressures of 0.21, 4.39, 9.97, 20.01, and 29.32 bar. By using a Pt NMR thermometer, an LCMN thermometer, and a³He melting curve thermometer calibrated using the melting curve given by Greywall in 1983, a temperature scale has been established and (1) it has been shown that this melting curve is consistent in the temperature range 5–22 mK with the Korringa law for the Pt thermometer with a Korringa constant of 29.8±0.2 sec mK, (2) departures have been observed from the Curie-Weiss law for LCMN at low temperatures, and (3) values of the superfluid transition temperature have been obtained that are about 4% lower than the Helsinki values. The measured heat capacities agree well with those of Greywall, but values ofKT are higher than those of Greywall and show more temperature dependence below 10 mK. The implications for the present results of the very different melting curve given by Greywall in 1985 are discussed in an Appendix.     

Thermal boundary resistance between liquid helium and silver sinter at low temperatures

We present measurements of the thermal coupling between Ag sinter (nominal grain size 700 Å) and superfluid³He-B atp = 0.3, 10, and 20 bar as well as a phase-separated³He⁴-He mixture atp = 0.5 bar in the submillikelvin regime. In order to analyze the data of the pure³He-B sample with respect to different contributions to the thermal resistance, a one-dimensional model for the heat flow in the sinter is presented. As a result it is shown that the thermal conductivity of the liquid in the sinter has to be taken into account to extract the temperature and pressure dependence of the boundary resistance in the confining geometry of the sinter. Depending on the value of this thermal conductivity, a boundary resistance proportional toT ^–2 orT ^–3 is found. Moreover, it is shown that a pressure dependence of the boundary resistance might be explained by a pressure dependence of the thermal conductivity of the liquid in the sinter. The data on the phase-separated mixture are equally well described by aT ^–2- and aT ^–3-dependence of the boundary resistance. We point out that a common problem in most measurements of the Kapitza resistance performed so far is the small temperature interval investigated, which usually does not allow a definite conclusion concerning the temperature dependence.     

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.     

A microscopic calculation of the force on a wire moving through superfluid3He-B in the ballistic regime

When a macroscopic object moves through superfluid³He, it experiences a force arising from the effect of quasiparticle scattering. We develop a three-dimensional microscopic model to calculate the force on a smooth cylinder moving at constant velocityv as a model of a vibrating wire. At large (subcritical) wire velocity, the force tends to an asymptotic value as 1/v ², rather than exponentially as in a one-dimensional calculation. At lowv the force is linear inv. We briefly discuss the agreement of our calculations with experimental measurements on a vibrating wire below 0.2T _c, where the quasiparticle trajectories are ballistic.     

Thermal convection and nonlinear effects of a superfluid3He-4He mixture in a porous medium

The convective instability of superfluid³He-⁴He mixtures in porous media is investigated. The general hydrodynamic equations are derived and reduced to a single nonlinear equation for a scalar field. The superfluid mixtures in a porous medium have a constant⁴He chemical potential and behave essentially like a classical fluid in a porous medium. Two-fluid effects are calculated both at the onset of steady convection and the subsequent boundary of instability. The shift of critical Rayleigh number is about 1% or less at the onset of convection, but can be as large as 20% or more at the instability boundary for some regions aroundT 1 K. This two-fluid shift is quite large compared to the corresponding 0.001% shift at the onset of convection for bulk superfluid³He-⁴He mixtures.     

Viscosity of the3He-4He dilute phase in the mixing chamber of a dilution refrigerator

The viscosity of the dilute phase of a³He-⁴He solution has been measured using a vibrating wire viscometer situated in the mixing chamber of a dilution refrigerator. The viscosity was extracted from the damping of the resonator for temperatures between 3.7 mK and 100 mK. In the low-temperature Fermi liquid regime T²=48×10^–9 N sec m^–2 K². For temperatures less than 100 mK, the viscometer is a useful secondary thermometer that is not strongly dependent on the applied magnetic field.     

Measuring the Decay of Vorticity in Superfluid 3He-B - A Progress Report

Recent measurements in superfluid ³ He-B have been interpreted as evidence in support of the Kibble-Zurek hypothesis for the formation of defects in the early Universe. The superfluid ³ He analogue to the cosmic string is the quantum vortex. We report here the preliminary attempts to detect the heat evolution from the decay of this vorticity in superfluid ³ He-B at temperatures down to 110 K. We produce vorticity by neutron irradiation of a small superfluid ³ He-B sample and attempt to measure the heat released as the vorticity decays. We detect a long time scale heat release and find that the lifetime of this decay varies inversely proportional to the quasiparticle excitation number density in the superfluid. However, we have yet to be convinced that this heat is from the decay of vorticity.     

Kapton Capacitance Thermometry at Low Temperatures and in High Magnetic Fields

A sensitive Kapton foil capacitance sensor, with size of 9.5 mm×4.5 mm, has been developed and used as a thermometer at ultra-low temperatures down to 1.2 mK and in high magnetic fields. There is no visible magnetic field dependence up to 15 T. The sensor was calibrated with ³He melting pressure thermometer (MPT) and vibrating wire (VW) viscometer. With the silver powder sintered heat exchanger sandwich-like design, the thermal relaxation time is as short as a few minutes at the base temperature. The low temperature (below 1.2 K) reproducibility has been tested and is satisfied within experimental errors.     

Baryon Asymmetry of Universe: View from Superfluid 3He

The origin of the excess of matter over antimatter in our Universe remains one of the fundamental problems. Dynamical baryogenesis in the process of the broken symmetry electroweak transition in the expanding Universe is the widely discussed model where the baryonic asymmetry is induced by the quantum chiral anomaly. We discuss the modelling of this phenomenon in superfluid ³ He and superconductors where the chiral anomaly is realized in the presence of quantized vortex, which introduces nodes into the energy spectrum of the fermionic quasiparticles. The spectral flow of fermions through the nodes during the vortex motion leads to the creation of fermionic charge from the superfluid vacuum and to transfer of the superfluid linear momentum into the heat bath, thus producing an extra force on the vortex, which in some cases compensates the Magnus force. This spectral-flow force was calculated 20 years ago by Kopnin and Kravtsov for s-wave superconductors, but only recently was it measured in a broad temperature range in Manchester experiments on rotating superfluid ³ He. The momentogenesis observed in ³ He is analogous to the dynamical production of baryons by cosmic strings. Some other possible scenaria of baryogenesis related to superfluid ³ He are discussed.     

Simulations of a Thermal Conductivity Cell Filled with Normal 4He and Dilute Mixtures of 3He in Superfluid 4He

We have simulated the thermal response of a cylindrical thermal conductivity cell filled with liquid helium to AC and DC heat fluxes. The conductivity cell in these simulations is realistic in that it includes sidewalls and gaps, which cannot be treated analytically or in a one-dimensional simulation. Our simulations are to able to account quantitatively for the apparent departure of the effective thermal conductivity, _eff , of dilute mixtures of ³ He in superfluid ⁴ He from theoretical predictions. We have recently demonstrated experimentally that this departure is due to the presence of gaps in previous thermal conductivity cells. These simulations also show that the additional phase lag in the response of normal ⁴ He to an AC heat flux, measured by Olafsen and Behringer, is due to gaps in the heated plate.     

The mechanical behavior of a vibrating wire in superfluid3He-B in the ballistic limit

An experimental procedure is described for the characterization of the response of very small vibrating wires to liquid³He at temperatures down to 120 µK. The relative scales of the mean free path in the liquid and the radius of the wire play a significant role in the interpretation of the results. It is shown that the same ideas concerning the transition from hydrodynamic to ballistic behavior as the temperature is reduced can be applied both to saturated³He-⁴He solutions and to superfluid³He-B.     

Motional states of3He and4He in the one-dimensional channels of K-L zeolite

The behavior of³He and⁴He in a one-dimensional channel (10 Å in diameter) of K-L zeolite has been studied by measuring isosteric heat of sorption and heat capacities in the temperature range 0.1–1.5 K as a function of the amount of helium adsorbed. At smaller amounts, below 40% of full channel, the He adatoms seem to be bound on the potential minima of the wall. However, at larger amounts adsorbed, between 40 and 70%, a one-dimensional translation of the excess adatoms over 40% is suggested by the results that the molar heat capacities atT1 K are about the magnitudeR/2 of a one-dimensional gas and that the heat of sorption atT=0 K is almost constant.Research Institute for Catalysis, Hokkaido University, Sapporo, Hokkaido, Japan.     

Specific heat of normal and superfluid3He

Extensive measurements of the heat capacity of liquid ³ He in the normal and superfluid phases are reported. The experiments range from 0.8 to 10 mK and cover pressures from 0 to 32.5 bar in zero magnetic field. The phase diagram of ³ He, based on the platinum NMR temperature scale, is presented. In the normal liquid at low pressures and near the superfluid transitionT _c an excess specific heat is found. The effective massm* of³He is at all pressures about 30% smaller than the values reported earlier. The calculated Fermi liquid parameters F₀ and F₁ are reduced asm*/m, while the spin alignment factor (1 + Z₀/4)^–1 is enhanced from 3.1–3.8 to 4.3–5.3, depending on pressure. The specific heat discontinuity C/C atT _c is forP = 0 close to the BCS value 1.43, whereas at 32.5 bar C/C is 1.90±0.03 in the B phase and 2.04±0.03 in the A phase, revealing distinctly the pressure dependence of strong coupling effects. The temperature dependence of the specific heat in the B phase agrees with a model calculation of Serene and Rainer. The latent heatL at the AB transition is 1.14±0.02 µJ/mole forP = 32.5 bar and decreases quickly as the polycritical point is approached; at 23.0 bar,L = 0.03 ± 0.02 µJ/mole.Work supported by the Academy of Finland.     

Optical interferometry at ultra low temperatures

We have developed optical, interferometric methods for investigations of interfaces at ultra low temperatures. In our scheme conventional optical windows are avoided: laser illumination (He-Ne) is guided into the cryostat via a single-mode optical fiber and images are taken using a CCD sensor mounted inside the 4-K vacuum can. A real-time video camera has been successfully used in investigations of superfluid³He down to 0.6 mK whereas a slow-scan camera has been employed for optimal contrast in low-intensity imaging of liquid/solid interfaces (reflection coefficient 10^–6). The investigated topics include (1) superfluid³He surface in rotation and during rapid deceleration, (2) hydrodynamics of thin superfluid³He layers, (3) superfluid/solid interface in⁴He, and (4) wetting of superfluid⁴He by normal³He in phase separated mixtures. A vertical resolution of 10 nm and even below has been achieved in these studies.