Quantum Fluid Dynamics of Rotating Superfluid 3He in Aerogel

Superfluid ³He A-like and B-like phases in 98% aerogel have been studied under rotation up to 2π rad/s by using cw-NMR and Homogeneous Pressing Domain (HPD) NMR at 29 mT and 3.0 MPa. Triplet superfluid ³He has continuous symmetries whose degeneracies are lifted by small perturbations of magnetic field, boundary condition of the sample cell, counterflow and global anisotropies of aerogel. We report NMR results of the two typical samples in aerogel under rotation, which are almost identical in the phase diagram, T _c and the critical velocity of the multiplication of vortex but are very different in textures and responses to the flow with each other. One samples (S-D) is slightly compressed by squeezing and thermal stress and thus has global anisotropic deformation along the sample axis. The other cell (S-H) has randomly(not uniaxially)-oriented global anisotropy. In the S-D, we observed a large negative shift in cw-NMR and spin wave and HPD in the B-like phase. Comparing textures determined by NMR and its response to the counterflows between two samples, we discuss how the long-range order of the continuous symmetry and textures are controlled by orientation effects due to global anisotropy in 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.      

NMR in Superfluid A-Like Phase of 3He Confined in?Globally Deformed Aerogel in?Tilted Magnetic Field

NMR spectra in superfluid A-like phases confined in axially deformed aerogel in the presence of a magnetic field inclined with respect to deformation axis is considered. The characteristic features of dipole frequency shift in axially compressed and axially stretched cases are compared. In particular, it is shown that in axially stretched aerogel environment the stability region of coherently spin-precessing mode is rather narrow due to the U(1) LIM effect. The spectrum of high-frequency spin fluctuations accompanying coherently precessing spin modes is constructed.     

Macroscopic Dynamics of the Polar Phase in Superfluid 3He

Recent NMR experiments on superfluid³He in an aerogel suggest that the superfluid phase found might be different from theA andB phases present in the bulk. Theoretical calculations indicate that the polar phase is the leading alternative candidate. In the present paper we derive the hydrodynamics of the polar phase. We study the influence of the magnetic dipole interaction and of a weak external magnetic field including thek=0 dynamics relevant for NMR. It turns out that cw NMR experiments can be used to distinguish the polar phase from theA phase provided one can orient the preferred direction of the polar phase in real space parallel and perpendicular to the container walls of an experimental cell. We also examine the influence of the presence of the aerogel on the reversible and dissipative hydrodynamics generalizing earlier work on superfluid⁴He in aerogels.     

Sound Experiments on Superfluidity of 3He in Highly Porous Aerogels

We have carried out sound experiments on superfluid ³ He in three highly porous aerogels with different porosities. Two of the acoustic cells contain aerogels inside the pores in roughly sintered silver powder to avoid the vibration of the aerogel. In these acoustic cells we have detected fourth sound, and extracted the superfluid density from the fourth sound velocity. The effect of the sintered silver on superfluid ³ He was examined by using another acoustic cell which contains the sintered silver without aerogel. The size of the pores in the sintered silver was large enough not to show the size effect of superfluid ³ He and small enough to observe fourth sound of ³ He. In another cell without sintered silver, we have observed second-sound-like signal. The superfluid transition temperatures of ³ He are suppressed more in higher density aerogel. The aerogel density dependence of the suppression of the superfluid transition temperature of ³ He in aerogel can be explained qualitatively by the simple s-wave scattering approximation. However, the superfluid density shows quite different pressure-dependence in different porous aerogels. The reason of this phenomenon is not understood yet.     

Evidence for Magnon BEC in Superfluid <Superscript>3</Superscript>He-A

The phenomenon of phase-coherent precession of magnetization in superfluid ³He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different states of coherent precession have been observed in ³He-B: homogeneously precessing domain (HPD); persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. Here we present evidence of magnons Bose-Einstein condensation in ³He-A in a compressed aerogel.     

Impurity Scattering Effect on Superfluid Phases of 3He in 97.5% Porous Silica Aerogel

No Heading NMR studies of superfluid ³He in 97.5% aerogel have been performed in a magnetic field of 28.4 mT. A small-angle neutron scattering experiment on the structure of the aerogel shows that the average separation distance of silica strands is 54 nm. The aerogel strands were covered with a few layers of solid ³He whose magnetization shows Curie-Weiss behaviour. On cooling process A-like phase appeared at suppressed superfluid transition temperature T_C^aero and B-like phase appeared at lower temperatures although only the B-like phase was observed up to T_C^aero on warming process above 2.1 MPa. The superfluid transitions in aerogel always occur below the AB phase transition temperature of bulk liquid at all pressures. An isotropic inhomogeneous scattering model(IISM) proposed by Thuneberg et al. explained well the observed suppressed T_C^aero in 97.5% with the radius 59 nm of voids in this model. This radius is similar with the average strand separation distance of 54 nm measured in the structural analysis. This similarity of two lengths shows the connection of the suppression of T_C^aero with the actual average separation distance of the silica strands.PACS numbers: 67.57.Pq, 67.80.Jd     

Vortex Core Contribution to Textural Energy in 3He�CB Below 0.4T c

Vortex lines affect the spatial order-parameter distribution in superfluid ³He?CB owing to superflow circulating around vortex cores and due to the interaction of the order parameter in the core and in the bulk as a result of superfluid coherence over the whole volume. The step-like change of the latter contribution at 0.6T _c (at a pressure of 29 bar) signifies the transition from axisymmetric cores at higher temperatures to broken-symmetry cores at lower temperatures. We extended earlier measurements of the core contribution to temperatures below 0.2T _c, in particular searching for a possible new core transition to lower symmetries. As a measuring tool we track the energy levels of magnon condensate states in a trap formed by the order-parameter texture.     

Transverse Acoustic Spectroscopy of Superfluid 3He in Compressed Aerogel

The unique nanoporous structure of aerogel provides a rare opportunity to study the role of anisotropic disorder on an anisotropic superfluid ³He. It has been proposed that uniaxial deformation of compliant aerogel would induce global anisotropy and a few compelling effects of global anisotropy on nature of the superfluid phases have been predicted. We measured high frequency shear acoustic impedance in superfluid ³He at 32 bar in a commercially available 98% porosity aerogel under uniaxial compression. At 5% compression, we found evidence of an A-like phase stabilized in a wider temperature width than the A-like phase in uncompressed aerogel.     

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.     

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.     

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.      

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.     

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     

Magnetic Susceptibility of the Balian–Werthamer Phase of 3He in Aerogel

The equilibrium superfluid phase of ³He impregnated into high-porosity (98%) silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian–Werthamer (BW) phase modified by the depairing effects of the aerogel structure. The nuclear magnetic susceptibility played a key role in identifying the B-phase of pure ³He with the BW state. We report theoretical calculations of the nuclear magnetic susceptibility for the BW model of superfluid ³He in aerogel within the framework of the Fermi-liquid theory of superfluid ³He. Scattering of quasiparticles by the aerogel, in addition to Fermi-liquid exchange corrections, leads to substantial changes in the susceptibility of the BW phase. The increase in the magnetic susceptibility of ³He-aerogel compared to pure³He-B is related to the polarizability of the gapless excitations and the impurity-induced local field. The limited data that is available is in rough agreement with theoretical predictions. Future measurements could prove important for a more definitive identification of the ordered phase, as well as for refining the theoretical model for the effects of disorder and scattering on the properties of superfluid ³He.     

The Tricritical Region for Helium Mixtures in 0.87 Porosity Aerogel

We have used ultrasonic velocity measurements to study ³ He- ⁴ He mixtures in aerogel with a porosity 0.87. The phase diagram resembles that of bulk mixtures, with a single transition for ³ He-rich mixtures, in contrast to the detached phase separation curve seen in 0.98 porosity aerogel. A kink in the lambda line at a 3He concentration of X _C =0.51 suggests that the phase separation line meets it at a tricritical point. We have measured the amount of superfluid which decouples both at low temperature and close to the superfluid transition, as functions of ³ He concentration. Each showed a sudden change at the concentration where the kink appeared in the lambda line, suggesting an abrupt change in the morphology of the superfluid phase in the mixtures. Similar measurements were made for pure 4He films on the same aerogel. We discuss the nature of ³ He-rich mixtures in aerogels based on these experiments.     

Scaling Properties of Superfluid 3He in Aerogel

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

Textures and Exotic Vortices in Neutral Fermion Superfluids

There has been intense interest in various Fermion superfluids in neutral atom liquids and gases, including chiral p-wave pairing in ³He-A phase and Feshbach-resonanced ⁶Li atom gases and d-wave pairing in atom gases. It is particularly interesting to find exotic vortices and associated low-lying Fermionic excitations under rotation. Here we report on our efforts of those topics: (1) Majorana Fermion in chiral superfluids near a p-wave Feshbach resonance. (2) Possible half-quantum vortices in p-wave superfluids of trapped Fermion atom gases. (3) Stability of a half-quantum vortex in rotating superfluid ³He-A between parallel plates. (4) Majorana bound state in rotating superfluid ³He-A between parallel plates. (5) Non-Abelian Fractional vortex in d-wave Feshbach resonance superfluids. We will summarize some of those works in a coherent manner in order to bridge the understanding between cold atom community and superfluid ³He community by stressing the importance of cross fertilization between them.     

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.     

The Equilibrium A-B Transition in Low Density Aerogels

No Heading We have measured in detail the NMR spectra of superfluid ³ He inside two different silica aerogels, one with a porosity of 99.3% and the other 98.6%. From these spectra, we are able to determine the equilibrium A-B transition temperatures in both aerogel samples as a function of hydrostatic pressure. We find that the slope of the reduced A-B transition temperature, 1- T_AB/T_c, vs. pressure is only about one third that seen for the bulk A-B transition, despite the fact the T_c for the two samples is suppressed very modestly, by only 4% and 8% at 34 bars. We argue from this that the presence of the aerogel stabilizes an equal-spin pairing which is district from that stable in the bulk.PACS numbers: 67.57 Pq, 67.57 Lm