A Preliminary Heat Capacity Measurement of 3He in Aerogel near its Superfluid Transition

We report simultaneous heat capacity and torsional oscillator measurement of ³ He in aerogel near the superfluid transition. The heat capacity has a peak at the temperature T_c where the torsional oscillator shows the onset of superfluid decoupling. The coincidence of these signatures suggests that ³ He in aerogel does undergo a true thermodynamic transition.     

Ultrasonic measurements as a probe of3He/4He phase separation in aerogels

We have used ultrasonic velocity and attenuation measurements to study the phase separation of³He/⁴He mixtures confined in a silica aerogel with a porosity of 87%. We used both shear and longitudinal sound and varied the frequency between 4 and 20 MHz. The superfluid transition is accompanied by a velocity increase due to decoupling and by a critical attenuation peak which increases with frequency. At the phase separation there are changes in the velocity and attenuation, and hysteresis on thermal cycling. We show some recent results and discuss how they relate to the phase diagram inferred from torsional oscillator and heat capacity measurements on helium mixtures in aerogels.     

Phase separation of3He-4He mixture in aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures confined in aerogel show evidence of a well defined phase separation region. This region is detached from the superfluid transition line, opening up a region of miscible superfluid mixture at high ³ He concentration.     

The Tricritical Region for Helium Mixtures in 0.87 Porosity Aerogel

We have used ultrasonic velocity measurements to study ³ He- ⁴ He mixtures in aerogel with a porosity 0.87. The phase diagram resembles that of bulk mixtures, with a single transition for ³ He-rich mixtures, in contrast to the detached phase separation curve seen in 0.98 porosity aerogel. A kink in the lambda line at a 3He concentration of X _C =0.51 suggests that the phase separation line meets it at a tricritical point. We have measured the amount of superfluid which decouples both at low temperature and close to the superfluid transition, as functions of ³ He concentration. Each showed a sudden change at the concentration where the kink appeared in the lambda line, suggesting an abrupt change in the morphology of the superfluid phase in the mixtures. Similar measurements were made for pure 4He films on the same aerogel. We discuss the nature of ³ He-rich mixtures in aerogels based on these experiments.     

Heat Capacity of Adsorbed Helium-3 at Ultra-Low Temperatures

We report on direct measurements of the heat capacity of monolayers of ³He adsorbed on the surface of a copper cell filled with superfluid ³He. We found that at ultra low temperatures the surface ³He heat capacity dominates over the heat capacity of the bulk liquid ³He. The replacement of adsorbed ³He by ⁴He changes the heat capacity of the sample by an order of magnitude. These investigations were made in the framework of the “ULTIMA” project, a dark matter detector based on superfluid ³He in the limit of ultra low temperatures.     

Self-Organized Heat Transport Near the Superfluid Transition in 4He

Heat transport through a column of superfluid ⁴ He has been observed experimentally to self-organize, resulting in a thermal gradient that exactly matches the gradient in the superfluid transition temperature across the column, leaving the entire sample at a constant distance from the superfluid critical point¹. We describe a new experiment that is designed to accomplish three objectives: 1) search for the upper critical heat flux above which self-organized heat transport can no longer occur, 2) measure the heat capacity of the self-organized heat transport state, and 3) test recent theoretical predictions^2,3 of the microscopic mechanism that is responsible for this self-organization.     

Measurements of the Superfluid Joule–Thomson Refrigerator Using High Concentration 3He–4He Mixtures

The superfluid Joule–Thomson refrigerator (SJTR) uses a liquid superfluid ³He–⁴He mixture to provide cooling below 1 K. Performance measurements of the SJTR using 5% and 11% ³He concentration mixtures are reported. High concentration operation shows higher cooling powers at high temperature. Ultimate temperatures are seen to increase with increasing concentration due to a pinching of the temperature defect in the recuperative heat exchanger. This pinching effect is due to the variation of the heat capacity of the ³He–⁴He mixture with temperature and concentration and is discussed in detail and design changes are suggested to mitigate it.     

3He-4He Mixtures in 95% Porous Aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures in 95% porous aerogel found a phase diagram similar to that in 98% porous aerogel. The coexistence boundary on the ³ He rich side resides very close to, but nevertheless is detached from the superfluid transition line. Together with the findings in 98%, 87%, and 99.5% porous aerogel, this result supports the interpretation that the phase separation of ³ He- ⁴ He mixture in aerogel is induced by the capillary condensation of ⁴ He films from neighboring silica strands into ⁴ He rich domains.     

Exact results for transport properties of anisotropic Fermi superfluids near the transition temperature

We discuss transport and relaxation processes in an anisotropic superfluid close to the transition temperature by deriving the quasiparticle Boltzmann equation. As an application we calculate the shear viscosity of liquid ³He exactly to first order in the superfluid gap, in terms of normal state properties. Exact results for the transport coefficients and relaxation rates in the super-fluid enable one to extract precise information about normal state scattering amplitudes from measurements in the superfluid phases.This research was supported in part by the National Science Foundation under grant DMR-7203026.     

The solubility of spin-polarized3He in4He and the superfluidity of3He in3He-4He mixtures

We investigate the possibility of a large enhancement of the T = 0 finite solubility of³He in⁴He due to spin-polarization. The size of the effect depends on the fraction of³He atoms in the system. We present two different approaches for the limits of a small and a large number of³He atoms compared to the number of⁴He atoms. Since the possible³He superfluid phase transition depends on³He density, we calculate the consequences of this change in the solubility for its superfluid transition temperature. It is shown that for small fractions of³He, the transition temperature is enhanced mostly due to the enlargement of the up-spin Fermi sphere. In the opposite limit the transition temperature is enhanced as a result of the increased³He solubility.     

Superfluid Phase Transition of 3He-4He Mixture Films Adsorbed on Alumina Powder

The superfluid phase transition of ³ He- ⁴ He mixture films adsorbed on 500 Å alumina powder has been studied for mixture films whose superfluid thickness is less than a monolayer. The transitions are found to be controlled by the Kosterlitz-Thouless critical line, but a strong broadening of the transition is observed as the ³ He concentration is increased. Analyzing the broadening in terms of a KT vortex-pair theory modified for the the finite powder size yields a vortex core parameter which increases nearly linearly with added ³ He. Also observed in these measurements is a temperature-dependent and ³ He-dependent depletion of the superfluid density at low temperatures, which is thought to arise from the high-frequency ripplon/third sound excitations of the film.     

Direct Observation of a Majorana Quasiparticle Heat Capacity in 3He

The Majorana fermion, which acts as its own antiparticle, was suggested by Majorana in 1937 (Nuovo Cimento 14:171). While no stable particle with Majorana properties has yet been observed, Majorana quasiparticles (QP) may exist at the boundaries of topological insulators. Here we report the preliminary results of direct observation of Majorana QPs by a precise measurements of superfluid ³He heat capacity. The bulk superfluid ³He heat capacity falls exponentially with cooling at the temperatures significantly below the energy gap. Owing to the zero energy gap mode the Majorana heat capacity falls in a power law. The Majorana heat capacity can be larger than bulk one at some temperature, which depends on surface to volume ratio of the experimental cell. Some times ago we developed the Dark matter particles detector (DMD) on a basis of superfluid ³He which is working at the frontier of extremely low temperatures (Winkelmann et al., Nucl. Instrum. Meth. A 559:384–386, 2006). Here we report the observation of zero gap mode of Majorana, follows from the new analyses of DMD heat capacity, published early. We have found a 10 % deviation from the bulk superfluid ³He heat capacity at the temperature of 135 μK. This deviation corresponds well to the theoretical value for Majorana heat capacity at such low temperature. (Note, there were no fitting parameters).     

Heat Capacity of Liquid 4He Confined in a Nanoporous Glass

We report a preliminary study of heat capacities of ⁴He confined in a nanoporous Gelsil glass that has nanopores of 2.5 nm in diameter. The heat capacity has a broad peak at a temperature far above the superfluid transition temperature obtained by torsional oscillator technique. The heat-capacity peak is attributed to formation of localized Bose-Einstein Condensates in the nanopores, in which the long-range superfluid coherence is destroyed by pore size distribution or random potential inherent to the porous glass.      

Heat Capacity Measurements of 3He-4He Mixture Films

We report heat capacity measurements from our on-going experiments on two-dimensional liquid ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He coverage dependence of the heat capacity for 0.02–0.50 bulk-density layers of ³He with 3.10 bulk-density layers of ⁴He over the temperature range 40≤T≤200 mK is presented. We find the effective mass of ³He on 3.10 layers of ⁴He is greater than that on 4.33 layers of ⁴He, consistent with our previous magnetic susceptibility measurements.     

Second-sound velocity and superfluid density in3He-4He mixtures near superfluid transition points—Applicability of universality and scaling laws

From second-sound velocity measurements, superfluid densities near superfluid transition points were determined in ³ He- ⁴ He mixtures under saturated vapor pressure. The critical exponent of the superfluid density thus obtained increases about 15% with increasing ³ He concentration up to 40 mole percent, which contradicts the universality concept. Furthermore, the critical exponents obtained here and the exponents of the specific heat do not satisfy the scaling laws. A new concept of universality is introduced and discussed.Submitted in partial fulfillment of the requirements for the Ph.D. degree at The University of Tokyo.     

Property of 4He Confined in 1D Nano-porous Medium FSM16 with 2.8-nm Channel Above Bulk Freezing Pressure

We have performed the freezing pressure and heat capacity measurements for ⁴He confined in a nano-porous medium FSM16 which possesses a one-dimensional 2.8-nm straight channel, in the pressure region above the bulk freezing pressure. At 2.8 MPa, where ⁴He in the channel remains a non-superfluid liquid down to the lowest temperature, the heat capacity decreases monotonically with decreasing temperature. It is in contrast to the heat capacity at 0.03 MPa with a broad bump at the temperature higher than the superfluid onset. At around the freezing onset in the channel, no clear heat capacity peak was observed. It suggests that the latent heat of the liquid?Csolid transition in the channel is quite small.     

Temperature and Concentration Relaxation in Phase-separated Superfluid 3He–4He Mixtures

The kinetics of the temperature and concentration variations in the superfluid ³He–⁴He mixtures with initial concentration of 9.8% ³He, and heated from below, was studied experimentally under the pressure of 0.38 bar over a temperature range of 150–400 mK. It is found that in contrast to homogeneous liquids, the temperature and concentration relaxation in phase-separated mixtures can be described by a superposition of two exponential processes in which the time constants of temperature and concentration variations coincide. If the initial mixture was homogeneous and phase separation was triggered by a heat flow, the temperature and concentration vary non-monotonically and exhibit anomalous features at the moment of phase separation. In this case the phase transition starts in the metastable superfluid, formed out of a quite supersaturated mixture where the nucleation of the new phase may be caused by quantized vortices. The results are analyzed in terms of two possible mechanisms of relaxation–the acoustic mechanism with the second sound velocity and the diffusive one connected with dissipative flows of impurity and thermal excitations. It is shown that the measured relaxation times agree with a prediction of the theory.      

4He in Nano-porous Media: Superfluidity and Quantum Phase Transition

This paper reviews recent findings of novel phenomena in ⁴He confined to a nano-porous glass. We examined pressure–temperature (P-T) phase diagram of ⁴He confined in a porous Gelsil glass that had nanopores 2.5 nm in diameter, by torsional oscillator and pressure studies. The obtained phase diagram is fairly unprecedented the superfluid transition temperature approaches zero at 3.4 MPa, and a novel nonsuperfluid phase exists between the superfluid and solid phase. These observations indicate that the confined ⁴He undergoes a superfluid-nonsuperfluid-solid quantum phase transition at zero temperature. We propose that the nonsuperfluid phase may be a localized Bose-condensed state in which global phase coherence is destroyed by a strong correlation between the ⁴He atoms or by a random potential. ⁴He in nanospace is an excellent model system for studying a strongly correlated Bose liquid and solid in a confinement potential.     

3He and 4He Coverage Dependence of FA 0 and FS 1 in Thin Mixture Films

No Heading We report additional heat capacity measurements and analysis from our experiments on two-dimensional liquid. ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He heat capacity for sub-monolayer coverages of ³He with 3.10 bulk-density layers of ⁴He for T 40 mK is discussed. We incorporate these measurements with earlier NMR work in similar coverage ranges and deduce preliminary values for the two-dimensional Fermi Liquid parameters for the ³He for 3.10 layers of ⁴He.PACS numbers: 67.60.Fp, 67.65.+z.