Anomalous Damping of a Low Frequency Vibrating Wire in Superfluid 3He-B due to Vortex Shielding

We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid ³He at zero pressure and at temperatures below 200 μK. The vibrating wire has a low resonant frequency of around 60 Hz. At low velocities the motion of the wire is impeded by its intrinsic (vacuum) damping and by the scattering of thermal quasiparticle excitations. At higher velocities we would normally expect the motion to be further damped by the creation of quasiparticles from pair-breaking. However, for a range of temperatures, as we increase the driving force we observe a sudden decrease in the damping of the wire. This results from a reduction in the thermal damping arising from the presence of quantum vortex lines generated by the wire. These vortex lines Andreev-reflect low energy excitations and thus partially shield the wire from incident thermal quasiparticles.     

Kelvin-Wave Cascades in Turbulent Superfluid 4He at Very Low Temperatures

There has been much interest recently in the mechanism by which superfluid (quantum) turbulence can decay in liquid ⁴He at very low temperatures, where mutual friction has a negligible effect. As in classical turbulence, energy must probably flow from larger to smaller length scales, and it has been suggested that on the smallest scales the relevant motion is a Kelvin wave on a quantized vortex with wave number greater than the inverse vortex spacing. By considering the behaviour of a simple model it is shown by computer simulations how energy can flow to shorter length scales (higher wave numbers) in a system of Kelvin waves, and how this process can lead to a remarkably simple Kelvin-wave energy spectrum. A discussion is included of the relevance of this model to the decay of superfluid grid turbulence at a very low temperature.     

High-temperature cooling power of the superfluid stirling refrigerator

Above 1 Kelvin, the measured cooling power of the superfluid Stirling refrigerator is significantly greater than would be expected simply from a classical ideal gas of³He quasiparticles. Analysis shows that this increased cooling power is due to the presence of the⁴He excitations.     

Baryon Asymmetry of Universe: View from Superfluid 3He

The origin of the excess of matter over antimatter in our Universe remains one of the fundamental problems. Dynamical baryogenesis in the process of the broken symmetry electroweak transition in the expanding Universe is the widely discussed model where the baryonic asymmetry is induced by the quantum chiral anomaly. We discuss the modelling of this phenomenon in superfluid ³ He and superconductors where the chiral anomaly is realized in the presence of quantized vortex, which introduces nodes into the energy spectrum of the fermionic quasiparticles. The spectral flow of fermions through the nodes during the vortex motion leads to the creation of fermionic charge from the superfluid vacuum and to transfer of the superfluid linear momentum into the heat bath, thus producing an extra force on the vortex, which in some cases compensates the Magnus force. This spectral-flow force was calculated 20 years ago by Kopnin and Kravtsov for s-wave superconductors, but only recently was it measured in a broad temperature range in Manchester experiments on rotating superfluid ³ He. The momentogenesis observed in ³ He is analogous to the dynamical production of baryons by cosmic strings. Some other possible scenaria of baryogenesis related to superfluid ³ He are discussed.     

Thermal behavior of quasiparticles in3He-B

We describe experiments on the transport of heat within a cell cooled by nuclear demagnetization of copper and containing³He-B at temperatures between 0.1 and 0.4 T_C. Within the bulk liquid helium, heat is transported by ballistic quasiparticles. In this case the conventional concept of boundary resistance is not applicable to the analysis of the heat exchange between refrigerant and³He. Rather, the cell geometry plays the important role. A thermal breakthrough in the cell is observed under conditions of heat flow large enough that the spin-lattice Korringa link to the copper refrigerant nuclei becomes saturated. At this point the lattice temperature rises, allowing heat to be transferred rapidly around the cell within the copper lattice, short-circuiting the liquid helium. We develop a simple model of heat transfer by ballistic quasiparticles which describes well the principal experimental features.     

Vortices Observed and to be Observed

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional vortices in unconventional superfluids and superconductors, which have been observed or have to be observed, such as continuous singly and doubly quantized vortices in ³ He-A and chiral Bose condensates; half-quantum vortices (Alice strings) in ³ He-A and in nonchiral Bose condensates; Abrikosov vortices with fractional magnetic flux in chiral and d-wave superconductors; vortex sheets in ³ He-A and chiral superconductors; the nexus—combined object formed by vortices and monopoles. Some properties of vortices related to the fermionic quasiparticles living in the vortex core are also discussed.     

Cascade Process of Vortex Tangle Dynamics in Superfluid 4He without Mutual Friction

Recently the Kelvin wave cascade process in superfluid ⁴ He at very low temperatures was discussed. In this mechanism, the dynamics of the waves on the vortex lines plays an important role. In order to investigate this mechanism, we study numerically the dynamics of the waves on the reconnected vortex lines using the full Biot-Savart law. This work shows the reconnection of two vortices leads to the waves on the reconnected vortex lines. To discuss the energy of the waves on the vortex lines, the energy spectrum of the superflow before and after the reconnection is calculated.     

Theory of heat transfer between phonons and quasiparticles in dilute solutions of3He in4He

A calculation of the heat transfer rate between phonons and quasiparticles in solutions of³He in⁴He is described. The phonon-quasiparticle interaction of Baym and Ebner is used, and two processes contributing to the heat transfer are considered. One process is phonon absorption and emission with the excess momentum distributed among the quasiparticles by quasiparticle-quasiparticle interactions. The other is quasielastic scattering of the phonons by quasiparticles. Numerical results are presented for 0.1% and 0.5% solutions. The calculated heat transfer rate for the 0.1% solution is in agreement with the one reported experiment atT40 mK, but is too small at higher temperatures (50T60 mK).     

Vortex Tangle Polarized by Rotation

Almost all studies of vortex states in superfluid ⁴He have been concerned with either ordered vortex arrays driven by rotation or disordered vortex tangles driven, for example, by thermal counterfiow. In this work we study numerically what happens to vortices in the presence of both effects. We find that a rotating vortex array becomes unstable, exciting Kelvin waves when it is subject to a counterfiow which is parallel to the rotation axis and which is sufficiently large. After the initial growth of the instability, the vortices enter a new, statistically steady, turbulent state, in which the vortex tangle is polarized along the rotational axis. We determine the polarization of the tangle as a function of the rotation frequency and the counterfiow velocity.     

Identification of Kelvin Waves: Numerical Challenges

Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.     

Calculations of static properties of spin-polarized3He-4He mixtures

The theory of dilute mixtures of³He in⁴He that have been polarized by a strong magnetic field is developed. The interaction between the quasiparticles is taken to be constant, an approximation valid at low temperatures. The polarization of the mixture depends on the strength of the interaction. The internal energy, the specific heat, the osmotic pressure, and the velocity of second sound are also calculated. The specific heat is relatively insensitive to the interaction, but it does change significantly with magnetic field. The osmotic pressure is more sensitive to the effects of the interaction for some³He concentrations and temperatures. The velocity of second sound behaves qualitatively like the osmotic pressure. The measurement of these quantities as a function of temperature and magnetic field is discussed with a view to obtaining the strength of the interaction between quasiparticles.     

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.     

Phase transitions in the growth of4He films

Using a microscopic, variational approach we examine the growth of⁴He absorbed to graphite and alkali substrates. We find that superfluid layers are formed and their behavior as a function of coverage is closely related to the one of a purely two-dimensional superfluid. The growth of a new layer undergoes a phase transition from a cluster formation into the connected superfluid when the coverage is increased. Based on the important connection to the two-dimensional fluid we propose a microscopic theory of quantum vortices in⁴He films at zero temperature, in which single vortices are treated as quasiparticles. We calculate the energy needed to create the single vortex, vortex inertial mass, microscopic interaction between vortices and binding energy of the vortex-antivortex pair as a function of density. We predict that at the⁴He superfluid density less than about 0.037 Å^–2 the binding energy of the pair becomes negative, indicating a phase transition into a new state where vortex-antivortex pairs are spontaneously created.     

Percolative diffusion of dissolved3He atoms in He II through porous media

The diffusion of³He quasiparticles in a dilute³He-⁴He solution confined in the porous medium is discussed on the basis of the percolation theory. It is pointed out that when³He quasiparticles diffuse through the porous medium,³He quasiparticles feel the random potentials originating from the random distribution of channel radii connecting pores. Noticing that the³He concentration can be varied over a wide range in³He-⁴He solutions, we find that the chemical potential of³He quasiparticles is related to the bond percolation densityp of the porous medium. It is emphasized that the mobility edge for³He quasiparticles is different between up and down spins under high magnetic fields. A novel mechanism utilizing this characteristics is proposed to produce the degenerate Fermi system with a very high polarization ratio. A discussion is given of the spatial localization of dissolved³He atoms due to the quantum interference. It is suggested that the localization effect is realized by the NMR experiments at very low temperatures.     

Air-side heat transfer enhancement of a refrigerator evaporator using vortex generation

In most domestic and commercial refrigeration systems, frost forms on the air-side surface of the air-to-refrigerant heat exchanger. Frost-tolerant designs typically employ a large fin spacing in order to delay the need for a defrost cycle. Unfortunately, this approach does not allow for a very high air-side heat transfer coefficient, and the performance of these heat exchangers is often air-side limited. Longitudinal vortex generation is a proven and effective technique for thinning the thermal boundary layer and enhancing heat transfer, but its efficacy in a frosting environment is essentially unknown. In this study, an array of delta-wing vortex generators is applied to a plain-fin-and-tube heat exchanger with a fin spacing of 8.5 mm. Heat transfer and pressure drop performance are measured to determine the effectiveness of the vortex generator under frosting conditions. For air-side Reynolds numbers between 500 and 1300, the air-side thermal resistance is reduced by 35–42% when vortex generation is used. Correspondingly, the heat transfer coefficient is observed to range from 33 to 53 W m⁻² K⁻¹ for the enhanced heat exchanger and from 18 to 26 W m⁻² K⁻¹ for the baseline heat exchanger.     

Transport properties of spin polarized3He-4He mixtures

We have calculated the viscosity, thermal conductivity, and longitudinal spin diffusion coefficient in³He-⁴He mixtures which are spin polarized. The calculation applies to all temperature regimes. We have also calculated the Onsager cross coefficient which arises because of the coupling between heat and longitudinal spin currents. The interaction between³He quasiparticles is taken to be a constant as a first approximation. We have also investigated the changes brought about by allowing the interaction to vary with the momentum of the quasiparticle.     

Self-Diffusion in 3He crystals

Measurements of self-diffusion in bcc ³ He 24,20-24,80 cm ³/mole were carried out by a new method in the temperature range 0.4 - 0.8 K. The vacancy diffusion coefficient was obtained by comparison of the self-diffusion data and the vacancy specific heat. It is found out that the vacancy diffusion is independent of temperature, because of spin disorder in this region. The data obtained shows that vacancies in bcc ³ He are wide-gap quasiparticles.     

Preliminary Measurements of Andreev Reflection of Quasiparticles by Turbulence in Superfluid 3He

We present preliminary measurements of Andreev scattering of quasiparticles from turbulence in the B-phase of superfluid ³ He-B. The turbulence is generated by a vibrating wire resonator driven above its pair-breaking critical velocity. The vortices intercept a beam of quasiparticles generated by a nearby black-body radiator. A substantial fraction of the incident quasiparticles are retro-reflected back into the radiator by Andreev scattering processes. The resulting temperature rise within the radiator provides a direct measurement of the flux of quasiparticles Andreev reflected. The technique provides a sensitive probe of superfluid turbulence in the ultra-low temperature regime.     

Generation-Recombination Noise: The Fundamental Sensitivity Limit for Kinetic Inductance Detectors

We present measurements of quasiparticle generation-recombination noise in aluminium Microwave Kinetic Inductance Detectors, the fundamental noise source for these detectors. Both the quasiparticle lifetime and the number of quasiparticles can be determined from the noise spectra. The number of quasiparticles saturates to 10?μm^?3 at temperatures below 160?mK, which is shown to limit the quasiparticle lifetime to 4?ms. These numbers lead to a generation-recombination noise limited noise equivalent power (NEP) of 1.5×10^?19?W/Hz^1/2. Since NEP∝N _qp , lowering the number of remnant quasiparticles will be crucial to improve the sensitivity of these detectors. We show that the readout power now limits the number of quasiparticles and thereby the sensitivity.