Fourth Sound Measurement of Superfluid 3He in Aerogel

The fourth sound resonance experiment has been done on liquid ³He in 98.5% porosity aerogel. Aerogel was grown inside the pores among the sintered silver powder to avoid the vibration of the aerogel strands by the sound experiment. The measurement was performed at zero magnetic field and 27 bar. We observed the phase transition between the A-like and B-like phases and also their coexistent state. The A-like to B-like phase transition occurs not at a temperature but within a temperature band. In this band, the A-like phase gradually converts to the B-like phase. Possible picture of the coexistent state is discussed.     

Perturbative Study of Strong Coupling Correction in Superfluid 3He in Aerogel

The AB transition curve of superfluid ³He in aerogel often shows a positive slope dT _AB(P)/dP>0 over the measured pressures P, contrary to that of the bulk liquid. Bearing this behavior in mind suggestive of a unexpectedly strong reduction of the strong coupling (SC) correction due to the aerogel, we examine impurity effects on the SC contributions to the quartic term of the Ginzburg-Landau (GL) functional. Our analysis perturbative both in the repulsive interaction and the impurity scattering suggests that, in agreement with experimental data, the impurity scattering weakens the relative stability of the ABM state to the BW state and notably reduces the SC correction for the ABM phase.     

Textures of Superfluid 3He A-like and B-like Phases in Aerogel under Rotation

Superfluid ³He A-like and B-like phases in 98% aerogel under rotation up to 2π rad/sec have been studied by cw-NMR and Homogeneous Precessing Domain (HPD) NMR at 29 mT and 3.0 MPa. In the A-like phase, a large negative frequency shift was observed in the cw-NMR spectrum and no effect of rotation on the spectrum was found. In the B-like phase, the spin wave spectrum was observed when the sample was cooled through T _c under rotation and was affected by the counter flow due to the trapped vortices. The HPD was excited in a part of the aerogel sample but introduction of vortices into the sample by rotation or trapped vortices destroyed the HPD.     

Anisotropic Aerogels for Studying Superfluid 3He

It may be possible to stabilize new superfluid phases of ³He with anisotropic silica aerogels. We discuss two methods that introduce anisotropy in the aerogel on length scales relevant to superfluid ³He. First, anisotropy can be induced with uniaxial strain. A second method generates anisotropy during the growth and drying stages. We have grown cylindrical ∼98% aerogels with anisotropy indicated by preferential radial shrinkage after supercritical drying and find that this shrinkage correlates with small angle x-ray scattering (SAXS). The growth-induced anisotropy was found to be ∼90° out of phase relative to that induced by strain. This has implications for the possible stabilization of superfluid phases with specific symmetry.     

Absolute Ultrasound Attenuation Measurements in Superfluid 3He in 98% Aerogel by Direct Transmission

Systematic investigations on the effect of static disorder on p-wave superfluid ³He have been made possible by utilizing the unique structure of high porosity silica aerogel. For the past 10 years, a burst of experimental efforts revealed that three distinct superfluid phases exists. We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B-phase of the superfluid ³He in 98% aerogel. The absolute attenuation was determined by direct propagation of sound pulses through the medium in a wide range of temperatures, down to 200 μK, for sample pressures of 10 and 29 bars. Our results provide direct information on the zero-energy density of states of the superfluid phase in aerogel originating from impurity scattering.     

Analysis of Strong-Coupling Parameters for Superfluid 3He

Superfluid ³He experiments show strong deviation from the weak-coupling limit of the Ginzburg-Landau theory, and this discrepancy grows with increasing pressure. Strong-coupling contributions to the quasiparticle interactions are known to account for this effect and they are manifest in the five β-coefficients of the fourth order Ginzburg-Landau free energy terms. The Ginzburg-Landau free energy also has a coefficient g _z to include magnetic field coupling to the order parameter. From NMR susceptibility experiments, we find the deviation of g _z from its weak-coupling value to be negligible at all pressures. New results for the pressure dependence of four different combinations of β-coefficients, β ₃₄₅, β ₁₂, β ₂₄₅, and β ₅ are calculated and comparison is made with theory.     

Acoustic Properties of Normal Liquid 3He in 98% Aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation and sound velocity measurements in the normal state of liquid ³He in 98% aerogel. The absolute attenuation and sound velocity were determined by direct propagation of sound pulses through the medium in a wide range of temperatures, 2 mK<T<200 mK. Due to the scattering off the aerogel, the sound excitation remains as first sound over the entire range of temperatures and pressures studied. Unlike pure liquid ³He, the sound attenuation shows a minimum around 30–50 mK, depending on the pressure. We report our results of absolute sound attenuation measurements at 29 bars of sample pressure.     

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.     

Nonlinear Transport of Wigner Solid on Superfluid 3He–A

Electrons trapped on the surface of liquid helium form the Wigner solid accompanied with the periodic surface deformation (dimple lattice). Because of the soft surface, the Wigner solid shows unique nonlinear transport properties. Here we present the results of the nonlinear transport measurements of the Wigner solid on the superfluid ³He A phase at temperatures down to 200 μK in a magnetic field of 0.363 Tesla. The transition from linear to nonlinear behavior is observed as increasing the driving voltage. This behavior is very similar to those previously observed in the B phase and normal phase, and attributable to the deformation of the dimple shape caused by the strong damping of liquid ³He.     

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.     

The AB Interface in Superfluid 3He as a Simulated Cosmological Brane

We present measurements of the transport of superfluid ³He quasiparticle excitations in the ballistic limit at temperatures well below T _c , and an interpretation of unexpected results as an experimental simulation of cosmological processes. Using a variable magnetic field profile we stabilize a layer of A phase across a cylinder of B phase, creating both an AB and a BA interface. These highly ordered interfaces may provide an ideal laboratory analogy for the branes and anti-branes of current cosmology. It has been suggested that brane interaction and annihilation are involved in inflation in the early Universe and leave behind topological defects such as cosmic strings. In our experiments we have annihilated our AB/BA branes by ramping down the magnetic field to remove the A phase layer. We then find that the quasiparticles face an extra impedance owing to defects left behind in the B phase texture. This is the first definitive observation of such a phenomenon.     

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.     

A-B Phase Conversion and Coexistence of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He at 2.4 MPa in cylindrical aerogel by NMR method. When the liquid is cooled down from the normal state, the A-like phase appears below superfluid transition temperature T _c ^a which is suppressed in comparison with the transition temperature of the bulk liquid. With further cooling below the certain temperature T _ab,c ^a , the A-like phase is converted into the B-like phase gradually. Both phases stably coexist within about 90 μK. When you keep the temperature constant in which both phases coexist, the A-B phase conversion stops. With furthermore cooling, the whole liquid becomes the B-like phase. The cwNMR spectra at the coexistence state suggest that the B-like phase is not uniformly distributed in the A-like phase like a large number of small bubbles in a liquid, but separated as a whole from the A-like phase. By applying a field gradient which changes as a function of square of radius, we found that the A-like phase is in the edge part with a cylindrical shape and the B-like phase is in the central part with a columnar shape.      

Superfluid Phases of 3He in Aerogel

No Heading Formal derivation of criterion for selection of superfluid phases of ³He in aerogel is presented. At the strength of the derived criterion variation of the order parameter of B-like phase in magnetic field differs from that of B-phase of pure ³He. Possible observable consequence of this difference is discussed.PACS numbers: 67.57.Pq, 67.57.Bc, 67.57.De     

Suhl Instability as a Mechanism of the Catastrophic Relaxation in the Superfluid 3He–B

In order to explain catastrophic relaxation, bulk mechanism based on Suhl instability (J. Phys. Chem. Solids 1, 209, 1957) is studied. It is shown, that at sufficiently low temperatures homogeneous precession of spin becomes unstable in the whole region of tipping angles of spin 0≤β≤π. In comparison with the previous publication of Surovtsev and Fomin (J. Exp. Theor. Phys. Lett. 83, 410, 2006) the leading zero temperature increments for the angles θ ₀≃104°≤β≤π are found. Estimation of the temperature of transition to the unstable state for the angle of 105°, that corresponds to the region of tipping angles in homogeneously precessing domain (HPD), is made.     

Long-Range Order in the A-like Phase of Superfluid 3He in Aerogel

A mutual action of the random anisotropy brought in the superfluid ³He by aerogel and of the global anisotropy caused by its deformation is considered. Strong global anisotropy tends to suppress fluctuations of orientation of the order parameter and stabilizes ABM order parameter. In a limit of vanishing anisotropy fluctuations of ABM order parameter became critical. It is argued that still in a region of small fluctuations the order parameter changes its form to be less sensitive to the random anisotropy. For a favorable landscape of the free energy of superfluid ³He the fluctuations remain small even in a limit of vanishing global anisotropy and the long-range order is maintained.      

Sound Modes of Superfluid 3He in Aerogel

We present the results of experiments on sound propagation at audio frequencies in ³ He-filled aerogel. Sound modes were observed at temperatures of 0.8–100 mK in an aerogel sample of 98% porosity. We find that below T _c for superfluid ³ He in the aerogel matrix the speed of sound in the composite system increases by as much as 1.5%. Also below the aerogel T _c new modes appear which correspond to propagation speeds of up to 10 m/s.     

Robust Superfluid Phases of 3He in Aerogel

Within a phenomenological approach possible forms of the order parameter of the superfluid phases of ³He in the vicinity of the transition temperature are discussed. The effect of aerogel is described by a random tensor field interacting with the orbital part of the order parameter. With respect to their interaction with the random tensor field a group of “robust” order parameters which can maintain long-range order in the presence of the random field is specified. Robust order parameters, corresponding to Equal Spin Pairing (ESP) states are found and proposed as candidates for the observed A-like superfluid phase of liquid ³He in aerogel.     

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of ³He 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 ³He 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.     

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid ³He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid ³He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.