Observation of3He crystallization down to 1 mK using a cooled CCD camera

We describe a new setup for optical observations (particularly of helium crystals) at ultralow temperatures. It is conceptually different from the usual optical setups, which require the use of optical windows in the cryostat. Our optical system, including the light source and camera, is placed inside the vacuum can of a dilution refrigerator cryostat. We have succeeded in filming the growth of³He crystals in contact with the superfluid B phase, down to 1 mK. The optical system can easily be combined with a nuclear demagnetization stage, and a simple extension of the image transport system will allow us to study³He crystals in high magnetic fields. The entire setup is described, and some typical images are shown.     

An experiment to measure the diffusion of4He in4He in the Fermi liquid region

The diffusion coefficient D and the thermal diffusion factor T, for⁴He in liquid³He at low temperatures T, have recently been calculated by solving the Boltzmann equation derived from Fermi-liquid theory. As T 0, T approaches a constant and D varies as 1/T. Both transport coefficients are determined solely by a ₀ ³⁴ , the l = 0 forward scattering amplitude. Because a ₀ ³⁴ can be found from thermodynamic data, e.g. the solubility of⁴He in liquid³He, X ₄ ^sat , a strict test of the theory is possible. We have built an apparatus to measure D and X ₄ ^sat as functions of pressure and temperature. The ratio of the capacitances of two parallel plate capacitors measures the number of⁴He atoms diffusing out of the liquid into the superfluid film. A bellows initiates the diffusion by changing the pressure in the liquid and thus the equilibrium concentration. A change of 10^–8 in the⁴He concentration can be detected.     

Surface Effects of 4He Coating on the Viscosity and the Slip Length of Normal and Superfluid 3He

We have measured the viscosity, , and the slip length, , of normal and superfluid ³ He using a torsional oscillator with a thick sample space. We coated the oscillating surface with 2.5 layers of ⁴ He film to study how the ⁴ He thin film changes the scattering mechanism of ³ He quasiparticles at the cell wall at 5 bar and 21 bar. In the normal phase, the temperature dependence of the viscosity was changed a little by the ⁴ He film at 21 bar but no change was observed at 5 bar. The slip length was enhanced by ⁴ He coating at 5 bar. This enhancement indicates the increase of specularity of ³ He quasiparticles scattering at the oscillating surface. On the other hand, a reduction of the slip length was observed at 21 bar. In the superfluid phase, the temperature dependence of supports the existence of Andreev reflection even with ⁴ He film on the surface at 5 bar and 21 bar.     

The dielectric formalism for3He-4He mixtures

The microscopic theory of³He-⁴He mixtures with a Bose condensate is formulated in terms of the dielectric formalism. By expressing all correlation functions in terms of proper, irreducible contributions, one sets the stage for approximate calculations that will be consistent with various exact sum rules and Ward identities, just as in the case of pure⁴He. The present analysis includes a symmetry-breaking term that allows us to deal with the continuity equations properly, and is valid at finite temperature. As a specific application, we express the normal fluid density _N in terms of the static⁴He current-current correlation function. We also give the first formal proof that in the presence of a moving condensate, the³He atoms make no direct contribution to the superfluid flow.     

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.     

Cooling of3He-4He dilute solution down to 97 μK. Thermal boundary resistance between dilute solution and metal powder

We have cooled a³He-⁴He dilute solution down to 97 K, which is the lowest temperature ever been achieved in a dilute mixture. However, there is no sign of the superfluid transition of³He quasiparticles in the solution. In the sub-millikelvin region, we have measured the thermal boundary resistance between the solutions and sintered metal powder as a function of temperature T. We find that the thermal boundary resistence is proportional to T^–2 below 1 mK and that the resistance shows a strong dependence on magnetic fields below 0.1 T. These results suggest that the magnetic coupling is dominant in this temperature region. We have also estimated the heat leak into the dilute solution. It is found that the heat leak is proportional to the power of one third of inverse time, and the main source of the heat leak is ascribed to the viscous movement of³He quasiparticles.     

Nuclear magnetic relaxation of3He gas. II.3He-4He mixtures

Longitudinal relaxation timesT ₁ have been measured in³He-⁴He gas mixtures, using pulsed NMR, in the temperature range 0.6–15 K. Helium-3 number densities of the order of 10²⁴ atoms m^–3 were used. Relaxation takes place on or near the walls of the Pyrex sample cells and measurements ofT ₁ give information about the surface phases. A cryogenic precoating of solid molecular hydrogen was used to reduce the helium-substrate binding energy from 100 K on Pyrex to 13 K for³He and 15 K for⁴He. TheT ₁ data at high temperatures were similar to those observed previously in the pure³He-H₂ system. The presence of⁴He generally causedT ₁ to rise on cooling below 2 K due to the preferential adsorption of⁴He over³He at the surface. However,³He atoms that go into quasiparticle states in the superfluid helium film can be an extra source of relaxation. In uncleaned cells, relaxation probably takes place in quasiparticle states at the free surface of the superfluid film, which are bound with an energy of 5.1±0.3 K. Baking the Pyrex cells under vacuum and rf discharge cleaning the walls before sealing in the sample gas were found to increase the bulk gasT ₁ by two or three orders of magnitude. In a cleaned, sealed cell aT ₁ of 8 h was measured at 7.7 MHz and 0.8 K. In this case relaxation is probably occurring two or three helium layers away from the helium-hydrogen interface. It may be possible to observe a predicted minimum in the intrinsic dipolarT ₁ of the bulk gas by using a⁴He wall coating to suppress wall relaxation effects (which usually dominate the nuclear relaxation of the bulk gas).     

Superfluidity of Pure 3He and Mixtures of 3He and 4He in Aerogel

We describe new torsional oscillator experiments on ³ He confined in 98.2% open aerogel. In one, we monitored the superfluid fraction of pure ³ He at T << T _c while we gradually changed the sample pressure. The resulting change in density alters ₀ of the superfluid ³ He relative to the distribution of the length scales (correlations) of silica in the aerogel. We observed a T = 0 normal-to-super fluid transition at a pressure of about 6.5 bar, in marked contrast to the bulk where liquid ³ He is superfluid at all pressures. In the second experiment, we measured the temperature dependence of the ³ He _s at a pressure of 21.6 bar with different amounts of ⁴ He present in the cell. Adding 2-3% ⁴ He slightly increases both T _c and _s . We found that for ⁴ He concentrations between 2% and 34%, the ³ He T _c increases by a very small amount. However, _s , which for pure ³ He in aerogel at 0.5T _c is no more than 11%, falls by another factor of 7. This behavior (constant T _c , reduced _s ) is similar to that observed in granular superconducting films where the long-range order is controlled by phase coherence between adjacent grains.     

The Effective Mass and Binding Energy of 4He in 3He in the Fermi Liquid Region

We have measured the solubility of ⁴ He in liquid ³ He down to about 40 mK and at pressures from zero up to 24 atm. The solubility was obtained from the thickness of the superfluid film in contact with unsaturated solutions of ⁴ He in ³ He as a function of temperature. By fitting the solubility data to Fermi liquid theory, we obtained the parameters m ₄ ^* and as a function of pressure. Here, m ₄ ^* is the effective mass of ⁴ He in liquid ³ He and the difference in binding energy between ⁴ He in pure ⁴ He and ⁴ He in liquid ³He. This difference has a minimum near 10 atm. The average of the results for m ₄ ^* , at different pressures, is (1.3 ± 0.2)m ₄. This agrees with the many body calculations of de Saavedra et al., and with the Stokes hydrodynamic mass using the partial volume of ⁴ He in ³ He, v ₄ ^* . The partial volume was obtained by taking the derivative of with respect to pressure.     

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.     

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.     

3He in Aerogel – an Inhomogeneously Disordered Unconventional Superfluid

We have examined the superfluidity of ³ He in 98.2% porous silica aerogel with up to 34% ⁴ He at 21.6 bar. The mixture is phase-separated for ⁴ He fractions between 11% and 34%. The ⁴ He-rich, phase preferentially occupies the regions of highest silica density in the aerogel, thus modifying the distribution of the correlated disorder seen by superftuid ³ He. The ³ He T _c increases slightly with ⁴ He content while the superfluid fraction decreases rapidly. This behavior is inconsistent with that of ³ He in a homogeneously scattering medium and is analogous to that of a granular superconductor.     

Low Temperature Heat-Capacities of Liquid 3He Thin Films

We have measured the heat capacity of ³ He thin films adsorbed on graphite at an areal density of 15.0 nm ^–2 down to as low as 100 K. The second-layer ³ He behaves as a degenerate 2D Fermi fluid in the whole temperature range we studied. We observed no anomalous behavior in the heat capacity near 3 mK in contradiction to the recent report by other workers. This indicates that possible superfluid transitions would be below 100 K. Instead, a small and temperature-independent contribution to the heat capacity was observed, which we attribute to nuclear-spin degrees of freedom in glassy solid ³ He trapped in substrate heterogeneities.     

3He film flow on a round rim beaker

The superfluid properties of thin (100–150 nm) of³He were investigated by measuring the rate at which a beaker of liquid³He emptied itself through the adsorbed film, with the film thickness decreasing as the level dropped. A beaker rim with a semicircular cross-section was used to provide a well defined geometry and to avoid the effects of small scratches that may have affected earlier experiments. The film thicknesses were determined by Atkins' oscillaton measurements of⁴He films on the same surface. The superfluid transition temperature in the filmT _c ^F was suppressed below the bulk valueT _c ^B , and was close to being described by 2/(T _c ^F ) = , as expected for A-phase. The critical current density was more than an order of magnitude smaller than expected for pair-breaking. When a⁴He monolayer was adsorbed on the substrate, there was no suppresson ofT _c ^F .     

Conductivity of the Wigner Solid on the Free Surface of Superfluid 3He-B

We have measured the conductivity of the 2D electron crystal (the Wigner solid) trapped on the free surface of superfluid ³ He-B down to 230 K. The resistance R(T) greatly decreases as temperature T decreases, obeying Arrhenius' law, R(T) exp (–(T)/k _B T), with (T) which we assign to the superfluid energy gap. This reveals that the scattering of ³ He quasiparticles by the WS determines the transport. As the input voltage increases, an anomalous behavior dominates the resistance just below the superfluid transition. The WS provides a new experimental method for probing both the bulk and free surface of superfluid ³ He.     

Ultra-Low Temperature Magnetic Properties of Liquid 3He Films

We report measurements of the nuclear magnetization of submonolayer liquid ³ He films adsorbed on a graphite substrate (Papyex) preplated by a monolayer of ⁴ He. In the submilliKelvin temperature range we observe a substantial enhancement of the nuclear magnetization with respect to the degenerate Fermi Liquid value. The unusual temperature dependence of this new contribution to the liquid ³ He film magnetization agrees well with that expected from the theory of weak disorder in two-dimensional (2D) correlated Fermion systems. The effects of disorder and reduced dimensionality suppress the superfluid transition at least to below 180 K.     

3He in 99.5% Porous Aerogel at the Normal-Superfluid Transition

We have used a torsional oscillator to measure the superfluid density and dissipation near the superfluid transition of ³ He in aerogel of 99.5% porosity. We used a new cell (constructed at Penn State) for which the aerogel was grown in the pores of a 100 m silver sinter. The cell was tested with ⁴ He and showed no signs of the second-sound resonances that have interfered with previous torsional oscillator measurements. The measurements with ³ He, presented here, were taken at pressures of 1.34 and 4.13 bars. We observed values of _s / in the T 0 limit of 0.05 and 0.14 respectively. Our measurements show an increase in the dissipation on warming through T _c . This series of measurements is ongoing and temperature sweeps at various pressures are planned.     

A First Order Normal to Superfluid Transition: Prewetting in the 4He-Rich Film below Liquid 3He

We summarize our earlier work on the prewetting transition in the ⁴He-rich film in contact with liquid ³He at low temperatures. We make a new fit to the experimental data using a simpler assumption than previously. The strong pressure dependence of the jump in film thickness at the transition D^s _min(P) is quantitatively explained. It is due to the depletion of the ³He concentration in the superfluid film. This is caused by the van der Waals field of the wall. As a result of the pressure dependence, the prewetting line begins at a quantum (T=0) critical point at 13.2 atm. The T=0 dewetting pressure is predicted to be 32.5 atm. The low temperature phase diagrams for the system are drawn in the D^s vs pressure plane and in the plane (₄–₃) vs ₃, where ₄ and ₃ are the chemical potentials. We predict that the prewetting line is metastable above an applied pressure of 25.75 atm. Above this pressure, bulk hcp ⁴He crystals should appear.     

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.     

Thermal boundary conductance between the U2D2 solid and B superfluid phases of3He

We present the first measurement of the thermal boundary conductance, 1/R _B , between the U2D2 spin ordered solid and theB superfluid phases of³He. We find that 1/R _B is exceedingly high, roughly seven orders of magnitude greater than that between sintered silver powder and liquid³He. ForT<0.56 mK, 1/R _B appeared to be thermally activated, i.e. 1/R _B exp(–/k _B T), with =4.5(±0.5) mK, close to the superfluid gap energy. We also present a theory involving magnon-quasiparticle coupling as a model to explain the experimental observations.