Scaling Results for Superfluid 3He in 98% Open Aerogel

We present experimental observations of the suppressed superfluid transition temperature, T _ca , superfluid fraction, ρ _s /ρ and Leggett frequency of ³He-B in aerogel, Ω _Ba . We determine T _ca from mass decoupling and the vanishing of the frequency shift away from the Larmor frequency in our different samples and different laboratories. We find that the suppressed transition temperature for ³He in aerogel occurs at a sample dependent, but approximately pressure independent, length, , where T _c and ξ ₀(P), are the transition temperature and the pressure dependent zero temperature coherence length for bulk ³He. T _ca also occurs at a pressure independent value of the Leggett frequency of bulk ³He-B. Further, we find that when the superfluid fraction and square of the Leggett frequency are plotted against T _ca −T (and not (T _ca −T)/T _ca ), the results of each measurement nearly collapse on to a pressure independent but sample dependent plot, with no further scaling. When plotted on a log–log scale, both measurements exhibit power laws in the range 1.33–1.45.      

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.     

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     

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.     

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature T _c ^a is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/T _c ^a ) at 0.9T _c ^a as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.     

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.     

NMR Properties of a Possible Non-unitary State of Superfluid 3He in Aerogel

No Heading We discuss the NMR properties of a non-unitary state which has recently been proposed by Fomin as a candidate for the A-like phase of superfluid ³He in aerogel. The new state is robust against the anisotropic scattering by the aerogel strands. We solve Leggettts equation for the robust state. Two transverse resonances as well as a longitudinal resonance are obtained. We find that in the pulsed-NMR the free induction frequency depends on the tipping angle as (1 + cos ).PACS numbers: 67.57.Lm, 67.57.Pq,     

Fourth Sound Propagation in Superfluid 3He in Aerogel

No Heading Impurity effect on the fourth sound propagation in the superfluid ³He-aerogel system confined in a channel is discussed on the basis of a two-fluid theory in which phenomenological parameters are determined microscopically within the homogeneous scattering model.PACS numbers: 67.57.De, 67.57.Hi, 67.57.Pq.     

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.      

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.     

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.      

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.     

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in superfluid ³ He at ultralow temperatures. The aerogel dik is attached to a goal post shaped vibrating wire resonator and immersed in liquid ³ He cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below <0.11T_c. At higher pressures we observe large temperature dependent frequency shifts, reminiscent of torsional oscillator experiments. We find the transition temperature at 5 bar to be around 600K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of ³ He in aerogel in the ultralow temperature regime.     

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.      

Collision Drag Effect on Two-Fluid Hydrodynamics of Superfluid 3He in Aerogel

Sound propagation in superfluid ³He in aerogel is studied on the basis of a two-fluid model taking into account the effect by the drag force due to collisions between ³He-quasiparticles and aerogel molecules. The drag force plays a role of frictional force between the aerogel and the normal-fluid component. In local equilibrium, they move together in accordance with McKenna et al.'s model. The deviation from the local equilibrium leads to the damping of sound. We give explicit expressions for the attenuation of longitudinal sounds in this system. We also discuss the sound propagation in a superfluid ³He-aerogel system embedded in a narrow pore. It is shown that the fourth sound propagates in such a system because of the clamping of the normal fluid by the aerogel.     

Possible Existence of Dense Superfluid 3He-4He Mixture in Aerogel

While studying superfluid ³He of 2.4 MPa in 97.5 %-porosity aerogel with NMR/MRI techniques, we find that the T _C is reduced when more than adequate amount of ⁴He, which covers the surface of silica strands, is introduced. For a sample, whose T _C is reduced to as low as 0.9 mK, we find that the spin diffusion coefficient in the normal phase is increased by a factor of 1.56 both in high temperature region, where ³He-³He scattering dominates, and in low temperature region, where ³He-aerogel scattering dominates. This enhancement is attributed to a modification of Landau parameter $F_{0}^{a}$ from ?0.757 to ?0.62, which is a change towards less ferromagnetic direction. The modification of microscopic quantity could be explained if small amount of ⁴He has homogeneously mixed into liquid ³He in 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.      

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.     

Non-linear Mechanical Response of the A-like Phase of Superfluid 3He in Aerogel

We present measurements of the response of the A-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 low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.