Magnetic Field Dependence of the A-like to B-like Transition of Superfluid 3He in Aerogel

Longitudinal ultrasound attenuation of superfluid ³He in 98% aerogel has been measured at 33 bar and 6.22 MHz in the presence of magnetic fields up to 4.44 kG. The A-like to B-like (A-B like) phase transition in aerogel was identified by a rounded jump in attenuation while sweeping the temperature at a fixed magnetic field perpendicular to the direction of sound propagation. The suppression of the B-like phase was monitored as the magnetic field increased until the A-like phase region extended below our lowest attainable temperature (0.2 mK) at the highest field. In addition, the attenuation in the metastable A-like phase that appears when cooling in zero magnetic field was almost identical to the values observed in the A-like phase in high magnetic field.     

Thickness Dependence of Critical Current of Superfluid 3He Film

We have measured the critical current J _c , which is defined as the onset of dissipative flow, for a thickness range from 0.3 to 4 μm using inter-digitated capacitors. In the thickness dependence of J _c , two distinct dissipation regimes were observed. The crossover occurred at a thickness of ∼1 μm.     

Vortex Core Transitions in Superfluid 3He in Uniaxially Anisotropic Aerogel

Vortex core transitions (VCTs) in the superfluid phases of liquid ³He in uniaxially stretched and compressed aerogels are theoretically investigated. Uniaxial deformation imposed on the aerogel alters superfluid pairing symmetries in aerogels and the axial and polar pairing states are favored. In this study, we examine whether the effects of the uniaxial anisotropy on the pairing symmetries are reflected in core states of a single vortex extending along the deformation axis. By numerically solving the Ginzburg-Landau equations, we find that in the compressed aerogel, the first order VCT appears at any pressure in the B-like phase, while in the stretched aerogel, the VCT in the B-like phase is lost. Further, the vortices in the A-like phase in the stretched aerogel, have a polar core state in place of the A-phase core of the nonsingular Mermin-Ho vortex.     

Spin Pumping Effect in Superfluid 3He A1

A fountain effect is a common phenomenon in both ³He and ⁴He superfluids. Unique to superfluid ³He is the magnetic fountain effect, which has been used to determine the spin direction of the condensate in ³He A₁ phase. Here we present a pressure driven fountain effect in A₁ phase. The experimental cell is composed of a large reservoir connected to a small detector chamber through superleak channels of width of 20 μm. One wall of the detector chamber houses a movable circular 6 μm thick membrane which serves as a sensitive capacitive pressure sensor and also acts as a spin pump. In A₁ phase, a DC voltage applied on the capacitor induces a simultaneous mass and spin superfluid current into the small chamber. After equilibration, removal of the DC voltage causes a sudden pressure drop followed by a slow relaxation. The sudden drop is a consequence of reversed superfluid flow through the superleak. The observed decay times during the slow relaxation agree with those obtained in magnetically induced spin flow experiment. These observations show that the slow relaxation stems from spin relaxation in the absence of applied field gradient.     

Pressure Dependence of the Multiphonon Excitations of Superfluid 4He

The pressure dependence of the multiphonon excitations in superfluid ⁴He has been studied, using neutron inelastic scattering. High-resolution measurements have been made at 0,5 K over a wavevector range 0.6<Q<2.2 Å^–1, at various pressures between 0 and 20 bars. The experimental data are presented and existing theoretical calculations are discussed.     

Substrate Dependence of the Superfluid Onset of 4He Films

We have performed torsional oscillator measurements of ⁴ He films adsorbed on porous gold and gold preplated with Ar, Ne, D ₂ , HD, and H ₂ . On all substrates, the superfluid response is similar. The thickness of the nonsuperfluid layer as function of the substrate, however, increases monotonically with the well depth of the atom-substrate interaction potential.     

Counterflow-Driven Textural Phase Transitions in Superfluid 3He-A1

We have studied second sound propagation through superftuid ³ He-A ₁ filling a rectangular resonator equipped with 3 pairs of transducers. The -texture was manipulated using one transducer to drive an oscillatory counterflow while measuring the resonant response of an orthogonal transducer pair. We observed abrupt signal changes and hysteresis effects depending on drive frequencies and amplitudes. We analyzed our experiments by examining planar -textures strongly coupled to the linear second sound wave equation. Evidence of first-order phase transitions was obtained numerically. The results are qualitatively consistent with the experimental findings. Our physical intuition did not anticipate these striking discontinuous phenomena.     

Negative Ion Mobility in Superfluid 3He Under High Magnetic Field

The negative ion mobility has been measured in superfluid ³He at pressures above 20 bar under high magnetic field up to 14 Tesla. It does not depend on the temperature in the normal phase, followed by a rapid increase below the superfluid transition in both A ₁ and A ₂ phase. The isothermal mobility is found to be independent of the magnetic field in the normal and A ₂ phase, while it decreases with increasing magnetic field in the A ₁ phase. This field dependence is explained by taking account of the field dependence of the transition temperature (T _{A 1}) between the normal and the A ₁ phase. Therefore the scattering cross section between, the negative ion and the ³He quasiparticles has no magnetic field dependence both in the superfluid and the normal phase.     

Excitations and Their Temperature Dependence in Superfluid 4He Beyond the Roton

The temperature dependence of the dynamic structure factor S(Q,) for superfluid ⁴ He has been measured by inelastic neutron scattering for wave vectors between 2.3 and 2.6 Å ^–l. S(Q,) has two peaks: one sharp peak at low energies whose dispersion flattens out and whose strength decreases with increasing Q, and one broader peak at higher energies with a stronger dispersion. The first peak disappears gradually with increasing temperature, while only part of the second peak vanishes at T . This indicates the existence of a third broad contribution, related to atoms above the Bose condensate. The two-peak structure can be interpreted in terms of a Bose-condensate induced coupling of the two-particle spectrum to the one-particle spectrum. The overall temperature dependence is consistent with the density-quasiparticle picture.     

The Wave-Vector Dependence of Quantum Evaporation from Superfluid 4He

Absolute measurements of the probability of quantum evaporation of atoms by rotons from the surface of superfluid ⁴ He are still problematic. However, it is possible to obtain information about the wave-vector dependence of the evaporation process by using a refined simulation ¹⁴ to interpret the experiments of Brown and Wyatt ¹² . Two theories (Guilleumas et al. ⁹ and Sobnack et al. ¹⁰ ) are compared with these experiments by incorporating their predictions for the quantum evaporation probability into a numerical simulation. Both theories over-estimate the probability of phonon-atom evaporation. For roton (R ⁺ –atom) evaporation, compared with a simulation that assumes all kinetically allowed events are equally probable, the theory of Guilleumas et al. does not significantly improve the agreement with experiment, and the theory of Sobnack et al. increases the discrepancy.     

Superfluid 3He in the Zero-Temperature Limit

Superfluid ³He has a hierarchy of properties, each manifest as a ‘superfluid’. There is the mass superfluid, the spin superfluid and there should also be an orbital superfluid. These three ‘super’ fluids respond differently to the interpenetrating normal fluid and demand different temperature ranges to be studied fully. We discuss here the importance of work at very low temperatures, how we can cool to the lowest temperatures and finally present a selection of low temperature experiments which illustrate aspects of multiphase nature of the superfluid and of the three ‘superfluids’ mentioned above. PACS numbers: 05.70 Ln, 05.70 Jk, 64.     

Positive Ion Mobility in Normal and Superfluid 3He at High Magnetic Field

We have measured the mobility of positive ions (snowballs) in liquid ³ He at magnetic fields H = 0 – 12 T and temperatures T = 0.3 – 10 mK. In normal ³ He, with increasing magnetic field the mobility first increases and then decreases nearly quadratically. The initial rise of the mobility is most strongly seen at the lowest temperatures (T = 2.5–3 mK) and high pressures (p = 29 bar) where at H = 6 T the mobility reaches a maximum enhancement of about 6 %. We attribute this effect to the suppression of the exchange scattering with magnetic field and thus infer the value of the exchange scattering cross-section. In the superfluid A ₁ and A ₂ phases, the relative increase of the ion mobility, as the sample is cooled below the transition temperature, is about twice as small as in the A or B phases.     

SH-SAW Sensor for Superfluid 3He

No Heading We have developed a new technique to study the transverse acoustic properties of superfluid ³He, employing a shear horizontal surface acoustic wave (SH-SAW) sensor. The transverse acoustic impedance can be obtained from the velocity and damping of SH-SAW which acoustically couples with liquid ³He all the interface. Since ultrasonic measurements provide the information about superfluid order-parameter through the excitation of collective modes, the SH-SAW sensor is expected to be a useful tool to study the boundary effect of superfluid ³He. Preliminary measurements were carried out at pressures of 17 and 23 bar, by the pulse transmission method at a frequency of 70 MHz. At 17 bar, imaginary squashing mode was observed as the sharp drop of the imaginary part of acoustic impedance. At 23 bar, the supercooled A-B phase transition was observed, as a jump of the real part of acoustic impedance, which was not observed in the warming process.PACS numbers: 67.57.Jj, 43.58.+z     

Superfluid3He in restricted geometries

It is shown that finite size effects stabilize a variety of phases in superfluid³He which do not occur in the bulk liquid. These phases are formed at temperatures at which the coherence length is comparable with the smallest linear dimension of the system. Right circular cylindrical geometries are considered explicitly.     

Induced Gravity in Superfluid 3He

The gapless fermionic excitations in superfluid ³ He-A have the relativistic spectrum close to the gap nodes. This allowed us to model the modern cos-mological scenaria of baryogenesis and magnetogenesis. The same massless fermions induce another low-energy property of the quantum vacuum – the gravitation. The effective metric of the space, in which the free quasiparticles move along geodesies, is not generally flat. Different order parameter textures correspond to curved effective space and produce many different exotic metrics, which are theoretically discussed in quantum gravity and cosmology. This includes the condensed matter analog of the black hole and event horizon, which can be realized in the moving soliton. This will allow us to simulate and thus experimentally investigate such quantum phenomena as the Hawking radiation from the horizon, the Bekenstein entropy of the black hole, and the structure of the quantum vacuum behind the horizon. One can also simulate the conical singularities produced by cosmic strings and monopoles; inflation; temperature dependence of the cosmological and Newton constants, etc.     

Electrons on the Surface of Superfluid 3He

A review of recent investigations of transport properties of surface state electrons on superfluid ³He is given. The surface state electrons in this temperature region form the Wigner solid (WS), a triangular lattice of electrons with a typical lattice constant of 1 μm. The WS is accompanied with a shallow corrugation of He surface commensurate with the WS. A model is introduced to interpret the observed WS resistivity. The model takes into account specular quasiparticle (QP) reflection from the moderately corrugated free surface, and treats the QP as if it is a quasiclassical particle. After adopting anisotropic properties of superfluid ³He order parameter and QP energy, the model provides satisfactory account of the observed properties. Preliminary results of mobility measurements of ions trapped below superfluid ³He-B are also given.     

Rotating Superfluid 3He in Aerogel

Rotational effects on textures of superfluid ³He in aerogel with 98% porosity at a pressure 3.0 MPa were investigated by cw-NMR measurement at 700 kHz (H ₀=22 mT) under rotation up to 2π rad/s. At rest, the superfluidtransition to the A phase occurred at T ^aerogel _c =2.07 mK and the A phase was supercooled down to T ^aerogel _A→B==1.73～1.80 mK and became the B phase in the cooling process. In the warming process, the B phase was superheated up to T ^aerogel _c . In the B phase, a new peak appeared in the NMR spectrum by rotating the sample. The intensity of this peak increased as the rotation speed increased almost linealy to Ω and started to be saturated for Ω≥Ω _c. We attributed the new peak to the textural change caused by the counter flow and the onset of the saturation at Ω _c to the onset of vortex nucleation in aerogel. On deceleration, the peak intensity decreased and disappeared at Ω=Ω _v. Further decreasing Ω, the peak intensity increased even at Ω=0. The counterflow peak observed at Ω=0 indicates the existence of persistent current induced by pinned vortices in aerogel. In the A phase, we did not find any noticeable change in the NMR spectrum under the rotation speed up to 2π rad/s, or by cooling through T _c with or without rotation. We concluded that the ${\hat \ell }$ texture in the A phase was strongly pinned to aerogel. No spin wave satellite signal localized at a soft, core vortex was observed in contrast to the bulk A phase.     

The Energy Dependence of Roton Quantum Evaporation from Superfluid 4He

We have measured the energy dependence of roton quantum evaporation. A transiently heated cavity filled with superfluid ⁴ He generates R⁺ and R^– rotons. The emitted rotons are collimated and arrive at the free liquid surface with a narrow range of incident angles. We detect two beams of evaporated atoms, one due to R⁺ rotons and the other due to R^– rotons. Our numerical simulation of roton and atom trajectories, using an evaporation probability of 1, yields two angular distributions of atom flux which are similar to our experimental results, but do have systematic differences which we attribute to the evaporation probability. The ratio of the observed signal to the computed value at each bolometer position gives the relative roton quantum evaporation probability as a function of roton energy. We find that this probability increases with roton energy, except perhaps for low energy R^– rotons. We compare these results with theoretical predictions.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

High-Energy Low-Temperature Physics: Production of Phase Transitions and Topological Defects by Energetic Particles in Superfluid 3He

I review three sets of experiments conducted in the last decade, in which superfluid ³ He was irradiated with high-energy particles and the nucleation either of vorticity or of the A–B phase transition reported. I consider how far the known atomic physics constrains possible scenarios for such nucleation, and comment on two such scenarios which have appeared in the literature, namely the baked-Alaska and cosmological (Kibble–Zurek–Volovik) models. I point out that there is a fundamental difference between the problems of nucleation of vorticity on the one hand and the B phase on the other: and that as a result, it is by no means necessary that the same scenario should describe both phenomena. In an appendix I discuss possible sinks of energy in the calorimetric (Grenoble–Lancaster) experiment, with the conclusion that it is entirely consistent with the data to assume that no vorticity at all was produced in this experiment.