Liquid 3He 4He Research Articles

Utilization of cryogenic phases of helium as “magic” working fluids in laboratory experiments: Pushing the boundaries of fluid dynamics

A surprisingly large part of the valuable scientific contributions of K. R. Sreenivasan—known to his friends and coworkers as Sreeni—to fluid dynamics is directly connected with precisely controlled benchmark experiments with cryogenic phases of helium. These experiments have been performed in a number of leading low temperature laboratories using conventional viscous 4He and 3He gases, normal liquid 4He (He I), as well as liquid 3He–4He mixtures and superfluid phases of 4He (He II) and 3He-B. We review their extraordinary physical properties and describe selected experiments, focusing on various forms of thermal convection, which push the boundaries of classical and quantum fluid dynamics.

The critical velocity of transition to turbulence in 3He–4He liquid solutions

The transition between laminar and turbulent flows around a quartz tuning fork vibrating with frequency ω in superfluid 4He and concentrated solutions (5 and 15% 3He in 4He) in the temperature range 0.3–2.3 K has been studied. The temperature dependences of the amplitude of the critical transition velocity vcr are obtained. The relationship vcr ∼ √(ηω/ρ) is shown to be applicable for the description of these dependences in concentrated solutions of 3He in 4He with density ρ and viscosity η, but this formula does not hold for the temperature dependence of vcr in pure 4He over the entire temperature range explored. It is also shown that in contrast to pure 4He temperature has virtually no effect in concentrated 3He–4He solutions on the drag coefficient in both laminar and turbulent regimes. The concentration dependences of the drag coefficient in the laminar regime normalized to the effective cross section of the vibrating body are plotted in the temperature range 0.5–1 K. The calculated dependences show that for low concentrations of a solution with x3 < 1% 3He the normalized drag coefficient weakly depends on the concentration of 3He and can be qualitatively described by the formula λ/S∼ρηω. In the x3 > 1% 3He concentration range, this coefficient increases sharply, and the reason for such a growth is currently not clear. Overall, the results of the study show that an increase in the 3He concentration in the solution enhances its stability with respect to the development of turbulence as the exciting force of a quartz tuning fork increases.

Anisotropic reduced diffusion in dilute liquid 3He–4He mixture in ordered aerogel

We report on the first observation of 3He diffusion anisotropy in 3He–4He liquid mixture confined in ordered aerogels at 1.5–4.2 K temperatures. The used aerogels are arrays of long Al2O3 parallel 8 nm strands. The possible origins of diffusion anisotropy are considered and the changes of roton properties introduced by parallel aerogel strands are discussed. Among the responsible mechanisms we account for Knudsen diffusion, potential anisotropy of layer mode excitations or of bulklike excitations, and helium vortices. The observed reduced 3He diffusion in aerogels is discussed and suggested to appear due to helium excitations at strong confinement conditions. These observations pave the way for future experiments to gain insight into the crossover regime expected at lower temperatures (below 1 K) for which roton density is lower and 3He collisions with strands play significant role.

Energy spectrum of surface electrons over the 3He–4He solution film with inhomogeneous isotope distribution

The energy spectrum of surface electrons localized over a 3He–4He liquid solution film covering a solid substrate is theoretically determined using the variational method. Two models of the spatial distribution of helium isotopes over the film height are considered. In one of them, it is believed that the film is stratified, and a continuous linear change in concentration is assumed in the second one. The potential energy of an electron is determined by the method of solving the Poisson equation for the electrostatic potential and in the gas approximation. Furthermore, it is established that the results of both methods practically coincide for a stratified film. The dependence of the energy gap between the ground and first excited states of surface electrons as a function of the film thickness is determined. Comparison of the results for the considered models of the film structure is carried out. The possibility of using the results obtained in an experimental study of the spatial isotopic distribution in a helium solution by the neutron scattering method is discussed.The energy spectrum of surface electrons localized over a 3He–4He liquid solution film covering a solid substrate is theoretically determined using the variational method. Two models of the spatial distribution of helium isotopes over the film height are considered. In one of them, it is believed that the film is stratified, and a continuous linear change in concentration is assumed in the second one. The potential energy of an electron is determined by the method of solving the Poisson equation for the electrostatic potential and in the gas approximation. Furthermore, it is established that the results of both methods practically coincide for a stratified film. The dependence of the energy gap between the ground and first excited states of surface electrons as a function of the film thickness is determined. Comparison of the results for the considered models of the film structure is carried out. The possibility of using the results obtained in an experimental study of the spatial isotopic distribution in...

Nucleation at quantized vortices and the heterogeneous phase separation in supersaturated superfluid 3He–4He liquid mixtures

Supersaturated superfluid 3He–4He liquid mixture, separating into the 3He-concentrated c-phase and 3He-diluted d-phase, represents a unique possibility for studying macroscopic quantum nucleation and quantum phase-separation kinetics in binary mixtures at low temperatures down to absolute zero. One of possible heterogeneous mechanisms for the phase separation of supersaturated d-phase is associated with superfluidity of this phase and with a possible existence of quantized vortices playing a role of nucleation sites for the c-phase of liquid mixture. We analyze the growth dynamics of vortex core filled with the c-phase and determine the temperature behavior of c-phase nucleation rate and the crossover temperature between the classical and quantum nucleation mechanisms.

Threefold reduction in thermal conductivity of Vycor glass due to adsorption of liquid 4He

We report thermal conductivity measurements of porous Vycor glass when it is empty and when the pores are filled with helium between 0.06 and 0.5 K. The filling of liquid 3He and liquid 4He inside the Vycor pores brings about two to three-fold reduction of the thermal conductivity as compared with empty Vycor. This dramatic reduction of thermal conductivity, not seen with solid 3He and 4He in the pores, is the consequence of hydrodynamic sound modes in liquid helium that greatly facilitate the quantum tunneling of the two-level systems in Vycor and enhance the scattering of the thermal phonons in the silica network.

Cryogenic electrolytes

Experimental evidence of metastable ion dipoles in solid helium is examined. Similar quasiparticles with positive scattering lengths for injected electrons are assumed to exist in the liquid phases of cryogenic liquids. Phenomena that can be used for detecting and monitoring a dipole gas in superfluid helium (referred to as cryogenic electrolyte) are discussed. The most interesting of these phenomena are: special features of the dielectric behavior of ion dipole gases, the temperature dependence of the ion dipole gas osmotic pressure at the boundary of liquid 3He-4He solution stratification, relaxation phenomena of collective origin in cryogenic electrolytes, and the transformation of the phonon spectrum of liquid helium owing to strong interactions between phonons and heavy dipole quasiparticles.

Liquid 3He–4He mixture phase diagram in restricted geometry

The influence of van der Waals forces on the decay of liquid solutions of helium isotopes is studied theoretically and the conditions for the phase co-existence in a confined geometry are investigated. As the models to account the influence of van der Waals forces on the helium isotope solution the gap between two parallel planes and the cylindrical channel are considered. For each of the models we calculated the concentration profile inside the channel depending on the van der Waals constant, the initial solution concentration and the size of the channel. The phase diagrams of liquid solutions are constructed. The obtained liquid mixture phase diagrams are compared with the “bulk” phase diagram. A rather good agreement between theoretical and experimental phase diagrams is obtained for liquid helium mixture in aerogel.

Negative ions at an interface between liquid helium mixtures

The properties of electron bubbles electrostatically forced against an interface between liquid 3He and saturated 4He–3He mixture were determined at low temperatures. The equilibrium state of such objects is characterized by the binding energy of 6.5 K and oscillatory spectrum of first excitations with a frequency of 0.6·1010 s–1. The shifting electric field E = 100 V/cm at the temperature T = 0.2 K leads to decaying the bound bubble state with the lifetime τ ≈ 1 s. The experimental study of bubble electron states can appear to be useful for determining properties of an interface between liquid helium mixtures.

Osmotic pressure of matter and vacuum energy

The walls of the box which contains matter represent a membrane that allows the relativistic quantum vacuum to pass but not matter. That is why the pressure of matter in the box may be considered as the analog of the osmotic pressure. However, we demonstrate that the osmotic pressure of matter is modified due to interaction of matter with vacuum. This interaction induces the nonzero negative vacuum pressure inside the box, as a result the measured osmotic pressure becomes smaller than the matter pressure. As distinct from the Casimir effect, this induced vacuum pressure is the bulk effect and does not depend on the size of the box. This effect dominates in the thermodynamic limit of the infinite volume of the box. Analog of this effect has been observed in the dilute solution of 3He in liquid 4He, where the superfluid 4He plays the role of the non-relativistic quantum vacuum, and 3He atoms play the role of matter.

Neutron reflection from the surfaces of liquid 4He and a Dilute 3He—4He solution

We report and discuss the first neutron reflection measurements from the free surfaces of normal and superfluid 4He and of a liquid 3He-4He mixture. In case of liquid 4He the surface roughness is different above and below the lambda transition, being smoother in the superfluid state. For the superfluid, we also observe the formation of a surface layer ∼ 200 Å thick which has a subtly different neutron scattering cross-section. The results can be interpreted as an enhancement of the Bose-Einstein condensate fraction close to the helium surface. We find that the addition of 3He isotopic impurities leads to the formation of Andreev levels at low temperatures.

Visual Observation of a Sound-Induced Bubble in Liquid 3He–4He Mixtures

We report visual observation of a sound-induced bubble in superfluid 3He–4He liquid mixtures using a high-speed camera at a rate of 1 msec/frame. The experiments were performed in the 3He dilute phase of phase-separated mixtures at 300 mK. The resonant frequency of the piezoelectric transducer was 9.36 MHz and the diameter of the active electrode was about 4 mm. When an acoustic wave pulse of sufficient magnitude was applied to the dilute phase from the transducer under saturated vapor pressure, a single bubble was nucleated on the active area. The bubble expanded almost spherically on the transducer, as it reached maximum size, it started shrinking, detached from the transducer, and collapsed. We also investigated the motion of the bubble in mixtures with a 3He concentration of 25% at 750 mK. In this case, the bubble grew elliptically on the transducer and detached from it without much change in shape.

Polarization Induced Spin Wave Damping in Spin Polarized Liquid 3He–4He

We have measured the temperature and polarization dependence of Silin spin wave spectra in a saturated 3He–4He mixture with a concentration of 9.4% at a pressure of 8 bars. The mixture has been cooled and polarized by a Leiden dilution refrigerator to temperatures in the range 10–15 mK and polarizations as high as 9.2% corresponding to 3.4 times the equilibrium polarization of 2.7% in the external magnetic field of 11.36 T. The analysis takes into account the dipolar interactions and results in the relaxation time τ⊥ and spin diffusion constant D⊥. We find that τ⊥ and D⊥ are proportional to \(1/(T^{2}+\mathcal{A}^{2}T_{a0}^{2})\) where T is the temperature, \(\mathcal{A}\) is the polarization enhancement factor and Ta0 is the anisotropy temperature for the mixture at equilibrium in the external field. Our result Ta0=3.66±0.14 mK is 30% higher than the theoretical prediction for very dilute mixtures and is evidence for the existence of polarization induced relaxation of transverse spin currents.

Application of Surface Acoustic Wave Sensors for Liquid Helium-4 and Helium-3

A surface acoustic wave (SAW) sensor can be used to determine the acoustic properties of liquid He. We applied this sensor for liquid 3He and liquid 4He. Two kinds of SAW were used in this experiment, Rayleigh-SAW and shear horizontal SAW. The damping of Rayleigh-SAW was measured in liquid 4He. The results agreed well with the reported values of the acoustic impedance, and the superfluid transition was clearly seen. The damping and the phase shift of shear horizontal SAW were measured in the normal liquid 3He. Temperature dependence of the damping and the phase shift was analyzed by the viscoelastic model, and the results were compared with the transverse acoustic impedance in the normal 3He.

Measurement of the Solubility of 4He in Liquid 3He in the Fermi-Liquid Region

The phase separation temperatures of dilute solutions of 4He in liquid 3He in the Fermi-liquid region have been measured by detecting the 4He film formation sensitively. From the obtained solubility curve, the effective mass of 4He atom and the difference in binding energy of 4He in liquid 4He and in liquid 3He are proposed.

Spectroscopy of molecules in helium droplets

The work reviewed in the talk explores the possibilities of using molecules immersed in liquid helium as probes to study superfluidity on the microscopic level. For this purpose liquid 4He, 3He and mixed 4He/ 3He droplets consisting of 10 3–10 5 atoms have been doped with single molecules or a small defined number of molecules which form clusters in the droplet interior. The dopants were investigated with high-resolution optical spectroscopy. The electronic and rovibrational spectra show unusually sharp spectral lines and unexpected features such as a distinct gap between the zero phonon line and the phonon wing as well as the free rotations of single molecules. Both are not observed in colder nonsuperfluid 3He droplets and therefore are considered to be new microscopic manifestations of superfluidity. Spectroscopic studies of small p-H 2 and o-D 2 clusters surrounding a single chromophore molecule formed in the interior of the He droplets are also reported.

4He in Liquid 3He below 0.1 K: Measurements of the Solubility and Prewetting Transition

We have measured the solubility of 4He in liquid 3He down to ∼0.04 K at various pressures. The solubility was obtained indirectly, from the thickness of the superfluid film in contact with unsaturated solutions. We determined the film thickness from the ratio of two parallel plate capacitors with different gaps, immersed in the unsaturated liquid. The technique is described in detail, with its advantages and drawbacks, including the effects of the edge capacitance and capillary condensation. For use in interpreting the data, the adsorption area and the van der Waals potential of the cell walls were found by measuring the thickness of 3He and 4He–3He films under their vapor pressure. By fitting the temperature dependence of the solubility to the predictions of Fermi liquid theory, we determined the 4He effective mass m*4, the binding energy E4 and the partial volume v*4, as a function of pressure. At 24 atm, a prewetting transition was observed in the 4He-rich film in contact with the liquid 3He. The transition, which is related to a similar phenomenon discovered by Tholen and Parpia at very low temperature, is explained by a simple model. An Appendix describes a new derivation of the thermodynamic functions of 3He-rich mixtures in Fermi liquid theory.

Superfluid Joule–Thomson Refrigeration, a New Concept for Cooling Below 2 Kelvin

A new type of sub-Kelvin refrigerator, the superfluid Joule–Thomson refrigerator is discussed. The refrigerator uses the circulation of the 3He component of a liquid 3He–4He mixture through a throttle to provide cooling to temperatures of 0.5 K. A simple analytical model is developed to predict the cooling power for this refrigerator as function of temperature. In addition, cooling power predictions are made using the equations of state of Radebaugh. The models are compared and discussed. This refrigerator can provide cooling in a microgravity environment.

Phase Separation of Liquid 3 He– 4 He Mixtures in Porous Vycor Glass

We report our recent investigations of the phase separation of liquid 3 He– 4 He mixtures in the restricted geometry of porous Vycor glass using pressure measurements. The experimental cell is entirely filled with a Vycor cylinder and closed by a cold valve. We are measuring the pressure versus temperature by means of a capacitive pressure gauge. The results are discussed in comparison with the phase separation of helium mixtures in aerogel, 1 in particular with respect to the different ratio of substrate surface to liquid volume of both glasses.

Experimental and Theoretical Problems of the Quantum Phase-Separation Kinetics of Liquid 3 He- 4 He Mixtures

The nucleation of the3He-concentrated phase is analyzed at the phase-separation of a supersaturated liquid3He–4He mixture in a wide range of temperatures. The crossover from the classical kinetics to the quantum kinetics is considered. Besides the homogeneous bulk nucleation the nucleation under heterogeneous conditions due to the possible presence of quantized vortices is examined.