Basic connection between superconductivity and superfluidity

A basic and inherently simple connection is shown to exist between superconductivity and superfluidity. It is shown that the author's previously derived general equation, which agrees well with the superconducting transition temperatures for the heavy-electron superconductors, metallic superconductors, oxide superconductors, metallic hydrogen, and neutron stars, also works well for the superfluid transition temperature of 2.6 mK for liquid³He. Reasonable estimates are made from 10^–3 to 10⁹ K — a range of 12 orders of magnitude. The same paradigm applies to the superfluid transition temperature of liquid⁴He, but results in a slightly different equation. The superfluid transition temperature for dilute solutions of³He in superfluid⁴He is estimated to be l–10K. This paradigm works well in detail for metallic, cuprate, and organic superconductors.     

Atomic impact experiments with free helium-3 and helium-4 clusters

Free helium clusters with of the order of 10³ to 10⁷ atoms have been predicted to reach final temperatures of about 0.4 K in the case of⁴He, and of 0.15 K in the case of³He. In the first case, the clusters have to be expected to be superfluid, in the latter case to be normalfluid. Impact experiments with cesium atoms, which are calculated to be strongly repelled from inside liquid⁴He, and slightly from liquid³He, indicate cesium embedding into or onto⁴He clusters. Xenon atoms, calculated to be strongly bound to both quantum liquids, show incomplete momentum transfer to⁴He as well as to³He clusters at higher impact speeds.     

Superflow in 3He-B in the presence of a magnetic field at all temperatures

We calculate gap functions, superfluid densities, critical currents, and susceptibilities for the B phase of ³He in the presence of currents and a magnetic field. The distortion of the gap function is properly taken into account.     

Experimental Setup for Observation the Bose–Einstein Condensation of Magnons in Solid Antiferromagnets CsMnF3 and MnCO3

The Bose–Einstein condensation of magnons was observed in 1984 in superfluid ³He–B. The same phenomena should exist in solid magnetic systems. We describe here a partly digital experimental setup for studying solid antiferromagnets CsMnF₃ and MnCO₃ by pulse and continuous wave nuclear magnetic resonance. With this equipment, the Bose–Einstein condensation of magnons was observed for the first time in these single crystals.     

Gliding for Gold: The Physics of Winter Sports,by Mark Denny

A comparison of the basic properties of the superfluid phases of liquid ³He with those of electrons in Type I superconductors and of bosons in liquid ⁴He reveals their similarity and differences. This is followed by some examples of the liquid crystal and magnetic properties of superfluid ³He and an account of the relationships between the tensor order parameter and the collective modes of the superfluid phases. The article ends with some comments on our present understanding of quantum liquids.     

New kinds of superconductivity and superfluidity

Formation of self-organized macroscopic and periodic structures in a physical system of interacting fermions are derived from first principles. The system of structureless and chargeless fermions with magnetic moments can have four different phases. Two of these phases exhibit the totally unique phenomena typical for superconductivity and superfluidity as well as various kinds of structural singularities such as disgyrations in the superfluid ³He.     

Superfluid transition temperature in a Fermi gas with repulsion allowing for higher orders of perturbation theory

Higher-order perturbation-theory corrections to the superfluid transition temperature in a weakly nonideal Fermi gas with repulsion are determined. This involves calculating the contribution of third-and fourth-order diagrams in terms of the gas parameter ap _F to the effective interaction which determines the super-fluid transition temperature and also allowing for effects associated with retardation and renormalization of the polar part of the Green’s function. The expressions obtained provide evidence in support of attraction in the effective interaction in the second, third, and fourth orders of perturbation theory. It is shown that the critical temperature is mainly determined by second-and third-order terms of perturbation theory. Calculations are made of the superfluid transition temperature for a gas comprising neutral Fermi particles in a magnetic field. The limits of validity of the theory are analyzed and the possibility of applying the results to dilute solutions of ³He in ⁴He and neutral-particle Fermi gases in magnetic traps is discussed.     

Critical velocities and two mechanisms of transition in superfluid liquid He

Two mechanisms of transition of the superfluid liquid ⁴He to quantum turbulence regimes are proposed for the case when the influence of the normal fluid on superfluid flow is suppressed by introducing superleaks at the ends of the capillary. Using dimensional analysis it is found that in the roton mechanism the critical velocity depends on channel size as vc∝d−1/4, matching the experiments. For the second, super-flow mechanism, the analysis of independent parameters relevant for this phenomena leads to critical velocity depending on d as vc∝d−1. It is shown that turbulence for super-flow mechanism arises when a “quantum Reynolds number” exceeds some critical value which is about 10³ for 1D geometry. The dimensional analysis of the equation for critical velocity of superfluid flow without superleaks at the ends of the capillary is also presented.     

NMR on superfluid<Superscript>3</Superscript>He in aerogel

The transition to superfluidity of³He in high porosity (98.2%) acrogel has been observed by nuclear magnetic resonance techniques. The onset of the transition at all pressures above 13 bar is marked by a sharp increase in NMR frequency similar to that observed in bulk³He-A. This suggests that the aerogel/superfluid phase is highly homogeneous although both the transition temperature, T_c, and the amplitude of the order parameter are substantially suppressed. The acrogel strands are ≈ 50Å in diameter, much smaller than the superfluid coherence length. Consequently, we have attempted to interpret our observations as an impurity scattering problem. Based on our measurements of the magnetic field dependence of T_c it appears that both magnetic and potential scattering play important roles where the magnetic scattering can be associated with solid³He on the aerogel surface. This is determined by isotopic exchange with⁴He, a process which appears to stabilize a new superfluid state similar to the bulk B-phase.     

Equilibrium superradiance in a Bose gas

A model of free₄He atoms interacting with radiation exhibits an equilibrium phase transition in which the atomic ground-state Bose condensation is coupled to condensations of virtual photons and virtually excited atoms of the same macroscopic wavelength. The condensed phase has a twofold polarization degeneracy. It is suggested that this might furnish a mechanism for a discrete symmetry-related phase degeneracy of superfluid liquid⁴He required to explain the transition according to Tisza's generalized Gibbsian thermodynamics. A more realistic model would require inclusion of repulsive interactions.Supported in part by the National Science Foundation, Grant DMR76-17467.     

Superfluidity of 3He in aerogel at T=0 in a magnetic field

The transition of liquid ³He to the superfluid B phase in aerogel at T=0 is considered. It is shown that in a magnetic field, the quantum phase transition with respect to pressure is split in two. The amount of splitting δP is estimated. The components of the superfluid density tensor are calculated near the critical pressures. Zh. éksp. Teor. Fiz. 115, 754–762 (February 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Neutron star matter superfluidity and superconductivity

The possibility of superfluidity or superconductivity in neutron or proton subsystems in the nuclear-matter region in neutron stars is investigated. The energy gap and corresponding critical temperature and critical magnetic field is calculated or estimated as function of density or Fermi momentum. In the calculations are used reaction matrix elements calculated earlier by means of Brueckner theory by the author. The final results indicate that neutron superfluidity, corresponding specifically toS-state pairing, may exist in a low-density shell in the nuclear-matter region of a neutron star. There is probably anisotropic neutron superfluidity, corresponding to the³ P ₂ or the singletD state, for higher densities. Superfluidity or superconductivity, corresponding toS-state pairing for the proton subsystem, is quite likely in most of the nuclear-matter region. The expected temperatures and magnetic fields in neutron stars seem to be well below the estimated critical temperatures or critical magnetic fields corresponding to the calculated values of the energy gap. However, similar methods have earlier predicted a much too high critical temperature for liquid³He.     

Gauge group and phases of superfluid 3He

The p-wave phases of superfluid ³He are classified without the unitary constraint or the constraints on the net nuclear magnetization and the magnetic susceptibility.     

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Transverse and longitudinal nuclear magnetic resonance in superfluid <Superscript>3</Superscript>He in anisotropic aerogel

It is found that the properties of nuclear magnetic resonance of both superfluid phases of ³He in an anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It is also shown that, by proper squeezing, it is possible to attain a sample with isotropic NMR properties.     

Nanocluster magnetic gel in superfluid He-II

The first results of the study of the structure of an impurity oxygen gel in superfluid He-II and in normal liquid helium have been obtained by the small-angle neutron scattering (SANS) method with cold neutrons. The angular dependence of the neutron scattering intensity I(q) indicates that the characteristic sizes of nanocluster aggregates forming a dispersive system (backbone) of an oxygen gel sample are distributed from 1 to ≈100 nm. According to the estimates made, if the working cell with superfluid helium cooled below 1.8 K is placed in a magnetic field of H ≥ 200 G, the magnetic structure of the nanocluster sample of oxygen gel, which is formed at the condensation of the flow of gaseous ⁴He with the impurity of O₂ vapor on the surface of He-II, will be close to ferromagnetic.     

Metastability and superfluid fraction of the A-like and B phases of <Superscript>3</Superscript>He in aerogel in zero magnetic field

We report the low-frequency sound measurements of the metastable A-like (A*) phase of superfluid ³He confined within a 98% open aerogel matrix in zero magnetic field. The second soundlike (slow) mode provides an accurate determination of the superfluid fraction of (and the transition between) the A* and B phases. The A* and B phases exhibit stable coexistence in the presence of disorder, the ratio of their superfluid fractions (ρ _a ^A* /ρ _s ^B ) is much smaller than that of the bulk A and B phases, and argues that the A* and bulk A phases are distinct.     

Transverse and longitudinal nuclear magnetic resonance in superfluid 3He in anisotropic aerogel

It is found that the properties of nuclear magnetic resonance of both superfluid phases of ³He in an anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It is also shown that, by proper squeezing, it is possible to attain a sample with isotropic NMR properties. The text was submitted by the authors in English.     

The superfluidd transition temperature of a Fermi liquid: 3He and 3He4He mixtures

The superfluid transitions temperature is calculated from the microscopic theory of a Fermi liquid in terms of the Landau parameters and one unknown scale factor. Determining the latter from the observed transition in ³He leads to an estimate that the superfluid transition in ³He⁴He mixtures may be presently observable.