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.     

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.     

Specific Heat of 4He Confined in Cylindrical Micro-Channels and Near the Superfluid Transition

We present new measurements of the specific heat C _P of ⁴He confined in cylindrical micro-channels of diameter L=1.89 μm at saturated vapor pressure and near the bulk superfluid-transition temperature T _λ . The results, when combined with the specific-heat exponent α=−0.01264, and with the correlation-length exponent ν=0.6709 obtained from α by hyper-scaling, support the departure from a universal, size independent, scaling function reported before by Lipa et al. [J. Low Temp. Phys. 124(3–4): 443, 2001] for L=8.17 μm and 0.26 μm. In agreement with Lipa et al., we found that a size independent effective scaling function can be recovered within experimental resolution when an empirical effective correlation-length exponent is used. As expected from theory, well away from T _λ the temperature dependence of the suppression of C _P by the confining medium is consistent with a power law with an exponent equal to α+ν=0.658. The universal ratio of the suppression at equal distances below and above the transition was measured to be R _f2=2.3±0.2. This result is consistent with the theoretical value R _f2=2.06 obtained by Bhattacharyya and Bhattacharjee and is close also to the ratio R _ξ ≃2.7 of the correlation-length amplitudes.     

Gravitational Effects on Nonlinear Heat Transport Near the Superfluid Transition in 4He

We have recently observed nonlinear heat transport within 30 nK of the superfluid transition temperature using heat flux, Q, in the range 0.1 < Q < 2 erg/(s cm ² ). While Haussmann and Dohm (HD) accurately predict the initial departure of the thermal conductivity, , from the linear response region, is greater than expected very close to T . We anticipate that the nature of the thermal conductivity's nonlinearity may depend upon Earth's gravity in the low heat flux limit (Q < 0.5 erg/(s cm ² )). Comparison of our data to similar data to be taken in a microgravity laboratory will provide an experimental determination of the effect of gravity on nonlinear heat transport near the superfluid transition. The microgravity measurements will also permit the first experimental test of theories that do not consider gravitational effects, such as those by HD.     

4He Adsorption and Superfluid Transition on C60

We present adsorption isotherm data of⁴He on C₆₀ for 1.50 K<T<1.68 K determined by measurements of the frequency of quartz crystal microbalances (QCM’s) coated with C₆₀ films. We find a Kosterlitz-Thouless transition with a jump in the areal superfluid density close to predictions. By comparing the adsorbed⁴He on two QCM’s we derive an upper limit for the amount of⁴He intercalated into C₆₀ at low temperature of 0.05⁴He atoms per C₆₀ molecule. The low coverage portion of the adsorption data shows an apparent excess adsorption of⁴He onto the C₆₀.     

Scaling, Dimensionality Crossover, Surface and Edge Specific Heats in Confined 4He

We have studied the superfluid transition of ⁴He in situations where the growth of the correlation length is limited by a uniform spatial confinement. Under these conditions the critical behavior attained in the thermodynamic limit is greatly modified. One expects that data for similar confinement should scale with the correlation length. This is found to be true for the specific heat in planar confinement, 2D crossover, except in the region of the specific heat maximum and on the superfluid side. The modifications due to confinement depend on the details of the geometry. Studies of the specific heat with 1D and 0D crossover show the important role played by the lower dimension. Far from the transition the details of the confining geometry reveal contributions to the specific heat which can be attributed to surfaces and edges. Comparison of experimental resugts with theoretical calculations show agreement in some areas and disagreement in others.     

Dynamics of the Cluster of Vortex Points in Two-Dimensional Superfluid 4He

We have simulated the dynamics of cluster of quantized vortex points with the same circulation in two-dimensional superfluid ⁴He. In two-dimensional quantum turbulence, vortices are always distributed uniformly, but often form some clusters. We study the dynamics of a cluster at zero temperature and finite temperatures. At zero temperature the cluster rotates. The radius and the density of the cluster hardly change because of the conservation of the energy and the angular momentum. On the other hand, at finite temperatures, the cluster rotates with forming a lattice structure and expanding because of the mutual friction.     

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of ³ He in different samples of silica aerogel. Several of these samples have been characterized using x-ray imaging, yielding information about the microstructure of the aerogel. In comparing new measurements on a 99.5% sample with previous observations on the behavior of ³ He in 98% porous aerogel we have found evidence for a scaling of the superfluid transition temperature to the correlation length of the aerogel. Furthermore, the superfluid density exhibits a similar universal behaviour over a range of values of reduced temperature. We discuss these new results in the context of superfluid pairing in the presence of a correlated disorder, specifically focussing on the fractal nature of the aerogel.     

Observation of Crossover from Ballistic to Diffusion Regime for Excimer Molecules in Superfluid 4He

We have measured the temperature dependence of the time of flight of helium excimer molecules $\mathrm {He}_{2}^{*}(a^{3}\Sigma ^{+}_{u})$  in superfluid ⁴He and find that the molecules behave ballistically below ～100 mK and exhibit Brownian motion above ～200 mK. In the intermediate temperature range the transport cannot be described by either of the models.     

Superfluid Transition of a 4He Thin Film Pressurized by Bulk Liquid 3He

We measured transverse acoustic impedance Z of normal fluid ³He at 46.6 MHz on a surface coated with a thin ⁴He film. The real component of the impedance, Z′, in the coated samples deviates from Z′ in the pure ³He in the low temperature region. Z′ on the coated samples is almost identical with Z′ in the pure sample at high temperature and gradually deviates below a particular temperature T _onset . T _onset  is possibly the superfluid onset temperature of the ⁴He film pressurized by the bulk liquid ³He. The gradual decrease in Z′ means that the superfluid component in ⁴He film increases gradually, which is expected from the dynamic KT transition at high frequency. The thicker is the film, the higher is the T _onset . The range of T _onset we observed was between 40 and 160 mK. This is much lower than that at the saturated vapor pressure. Suppression of T _onset achieved by the applied pressure from bulk liquid ³He was presumably caused by the dissolved ³He in the film, thickening of the inert layers and/or by the strong correlation effect. The result shows that the specularity of ³He quasiparticle scattering is strongly affected by superfluidity of the ⁴He film.     

The Superfluid Transition and Vortex Dynamics in Submonolayer Superfluid 4He Films in Porous Glass Under Rotation

A combination of a rotating dilution refrigerator and high-Q torsional oscillator technique has been used to study dynamics of vortices in thin ⁴ He films adsorbed on the porous glass (d=1m pore size). Under rotation an additional dissipation peak with the amplitude proportional to the angular velocity is seen at the middle of the superfluid transition, on the low temperature side of the stationary peak which is present even at =0. We attribute this peak to the 3D Type vortices created in multiply connected ⁴ He film by the rotation. Peak shape of the rotation-induced dissipation could be interpreted as a freezing of the 3D vortices well below T _c     

Transition to Turbulence and Critical Velocity in Superfluid Solution of 3He in 4He

By the method of oscillating tuning fork, we carried out researches of the transition to turbulence in superfluid solution of 5% ³He in ⁴He at temperatures of 100 mK–300 mK. The critical velocity υ _c of the turbulence appearance is determined through measuring the volt-ampere characteristics. It is established that in the mixture the temperature dependence of the critical velocity is non-monotonous and differs strongly from that in pure ⁴He. Unlike ⁴He, the step-like anomalies on resonance curves were observed which, presumably, is connected with instability of the vortex system under the conditions where the core of the vortex is filled by the atoms of ³He. It is shown that such anomalies appear at the temperatures below 0.9 K, at the same time at temperatures below ～0.5 K they appear even at υ<υ _c .     

Quartz Microbalance Study of Thick 4He Film Near the Superfluid Transition

We present the resugts of a quartz microbalance measurement of a ～440 Å thick ⁴He film adsorbed on Au. This measurement confirms the resugt of an earlier capacitance measurement that showed a dip in the film thickness just below Ta due to the critical Casimir force. The magnitude of the dip in the two measurements agrees within 15% . In addition to the dip, we see a signal due to the onset of superfluidity in the film. An apparent peak in the film thickness, not observed previously, is also found coinciding closely with the bulk T _λ. This extra feature may be due to a sound resonance in the cell associated with the bulk fluid.     

Thermal Resistance of 4He Below but Very Near the Superfluid Transition

We report high-resolution measurements at saturated vapor pressure of the thermal resistivity R of superfluid ⁴He over the reduced-temperature range 3×10^–7<t1–T/T <3×10^–5 (T is the transition temperature for Q=0) and heat-current-density range 4<Q<200 W/cm². For smaller Q and t, no thermal resistance was detectable below a transition at T _c(Q)<T . For Q10 W/cm² we find that the results can be described well by R=(t/t ₀)^–2.8 K cm/W with t ₀=(Q/Q ₀)^0.904 and Q ₀=393 W/cm². Thus R has an incipient divergence at T which is, however, supplanted by T _c(Q) where R remains finite. The results imply RQ ^(m–1) with m=3.53±0.02. This differs from the original assumption m=3 of Gorter and Mellink, and from experimental results obtained well below T . However, it agrees with measurements by Leiderer and Pobell at larger currents and further below but still close to T . Our measurements could not resolve a critical heat current for the onset of resistance.     

Measuring the Heat Capacity of Superfluid 4He in the Presence of a Heat Flux Near Tλ: Progress and Prospects

It has been predicted that the heat capacity of superfluid ⁴ He will diverge strongly at a depressed transition temperature in the presence of a constant heat flux, Q. We have built a cell to measure this effect, and have taken preliminary measurements at various heat flux values. Our data indicate an enhancement of the heat capacity that varies as a function of Q. However, the temperature dependence of our measurements leads us to believe that our initial findings were affected by spurious heat flow.     

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.      

Opportunities for High-Resolution Measurements and Microgravity Research near the Superfluid Transition of Liquid 4He

Six years ago an experiment to determine the specific heat of liquid helium near the superfluid transition in a microgravity environment opened up a new era of very-high resolution measurements. Recently this led to the establishment of the Fundamental Physics Discipline by NASA for the support of microgravity research in low-temperature/condensed-matter physics, laser cooling and atomic physics, and gravitation and relativity. This paper describes very-high resolution and microgravity research in one particular sub-field of low-temperature physics, namely the superfluid transition of ⁴ He, in order to illustrate the diverse research opportunities which exist within the Discipline. The effect of gravity on this system will be illustrated. Projects carried out already and expected to be undertaken in the near future on critical phenomena, surface effects, and non-equilibrium phenomena, will be discussed. These include measurements of the specific heat and the thermal conductivity, both in bulk samples and finite geometries, of the singularity of the boundary resistance between helium and a solid surface, as well as of non-equilibrium effects due to finite heat currents.     

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature T _c ^a is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/T _c ^a ) at 0.9T _c ^a as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.     

Heat Capacities of Monolayer 3He Fluids Floated on A Superfluid 4He Thin Film

We have measured heat capacities of monolayer ³ He floated on a superfluid ⁴ He thin film (three atomic layers) adsorbed on graphite at low temperatures. The ³ He films behave as degenerate 2D Fermi fluids with m* 1.3m ₃, where m* is the quasiparticle effective mass and m ₃ is the bare mass of ³ He, in the whole temperature range we studied (1 T 80 mK). No anomalous behavior suggesting puddling nor other phase transitions is observed. In contrast to our previous measurements for pure ³ He films without the underlying ⁴ He film, the temperature independent heat-capacity contribution is not observed. This can be explained by the second-layer localized spins trapped on substrate heterogeneities being replaced by nonmagnetic ⁴ He.