Spin Entropy Wave Propagation in Magnetically Polarized Superfluid 3He

The Spin-Entropy Wave (SEW) is the second sound (normal-superfluid counterflow mode) propagation in the spin-polarized superfluid ³He A₁ phase. Measurement of the propagation velocity gives the anisotropy components of the superfluid fraction. The perpendicular anisotropy component of superfluid density is measured as a function of magnetic field up to 12 T at 21.5 bar. The attenuation in bulk A₁ fluid is measured and is compared with theory on the spin diffusion and other dissipative coefficients. An anomalous diverging attenuation is observed at the lower transition temperature of the A₁ phase. When the superfluid flow accompanying the SEW is directed parallel to the anisotropy $$\hat{l}$$ texture, the flow field distorts the texture. The distortion results in an unusual non-linear propagation phenomena in which the non-linearity is greatest at intermediate flow velocities but reverts back to linear propagation at larger flow velocities. A mechanical system of mass attached to a soft spring is developed to model the non-linear propagation. An experiment is devised to control the $$\hat{l}$$ texture with one SEW resonance mode and to measure the texture transformation with an independent mode in a rectangular cell. Evidence for first order transitions of $$\hat{l}$$ texture is presented.     

Observations of Vortex Emissions from Superfluid 4He Turbulence at High Temperatures

An immersed object with high velocity oscillations causes quantum turbulence in superfluid ⁴He, even at very low temperatures. The continuously generated turbulence may emit vortex rings from a turbulent region. In the present work, we report vortex emissions from quantum turbulence in superfluid ⁴He at high temperatures, by using three vibrating wires as a turbulence generator and vortex detectors. Two detector wires were mounted beside a generator wire: one in parallel and the other in perpendicular to the oscillation direction of the generator. The detection times of vortex rings represent an exponential distribution with a delay time t ₀ and a mean detection period t ₁. The delay time includes the generation time of a fully developed turbulence and the time-of-flight of a vortex ring. At high temperatures, vortices are dissipated by relative motion between a normal fluid component and the vortices, resulting that only large vortex rings are reachable to the detectors. Using this method, we detected vortex rings with a diameter of 100 μm, comparable to a peak-to-peak vibration amplitude of 104 μm of the generator. The large vortices observed here are emitted anisotropically from the generator. The emissions parallel to the vibrating direction are much less than those perpendicular to the direction.     

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.     

Superfluid 3He Confined to a Single 0.6 Micron Slab Stability and Properties of the A-Like Phase Near the Weak Coupling Limit

We present the first study of the phase diagram of a thick film of superfluid ³He confined within a nanofabricated slab geometry. This cryogenic microfluidic chamber provides a well-defined environment for the superfluid, in which both the regular geometry and surface roughness may be fully characterised. The chamber is designed with a slab thickness d=0.6 μm and 3 mm thick walls to allow pressure tuning of the effective confinement between 0 and 5.5 bar. Over this range the zero temperature superfluid coherence length, ξ₀, decreases by approximately a factor of two from 77 to 40 nm. Samples have so far been cooled to 350 μK. We use nuclear magnetic resonance (NMR) to ‘finger-print’ the superfluid order parameter, with the static field applied perpendicular to the slab. To enable us to resolve high quality NMR signals from the tiny amount of superfluid ³He in the slab, we have developed a spectrometer using a two stage SQUID amplifier with unprecedented sensitivity. Simple NMR zeugmatography allows the slab signal to be unambiguously distinguished from that of a small bulk liquid region near the fill line. The measured slab transition temperature, T _c ^slab , shows a suppression proportional to ξ ₀ ² , as expected theoretically, but the absolute suppression is less than expected. Below T _c ^slab , an A-like phase is stable over a significant temperature range. A transition temperature, T _AX , is measured on warming from a so far unidentified phase, occurring at lower temperatures, into the A-phase. At the pressures investigated (3 to 5.5 bar) the transition appears to occur at an approximately fixed value of the effective confinement d/ξ(T _AX ). In this geometry we predict that the A-phase will be stable to T=0 at zero pressure.     

A–BTransition of Superfluid 3He with a Film Geometry

We have performedcwNMR experiments on superfluid ³ He confined to a parallel-plate geometry with a m scale spacing for a wide pressure range. A static field was applied parallel or perpendicular to the plate surface. The spectra of two absorption signals, a main and a satellite, have been observed below the superfluid transition temperature in a parallel field. As the temperature decreased, the main signal decreased with shifts to higher frequencies, and the satellite grew with shifts to much higher frequencies. From the temperature dependence of these signals and the result in the perpendicular field, it is confirmed that the main signal and the satellite correspond to the A phase signal (ABM state) and the B phase signal (BW state), respectively. The temperature dependence of the two signals indicates that a phase transition from the A phase to the B phase occurs with decreasing temperature. By analyzing these signals, we determine A–B transition temperatures experimentaly. TheA–Btransition temperature normalized by the superfluid transition temperature is 0.95 at 20 bar, and decreased further to 0.70 at 0 bar for a thickness of 0.88 m for pure ³ He. The values of T_AB/T_C were slightly elevated when covering the surface with 4.5 layers of ⁴ He film, which suggests that this transition is also influenced by the surface condition.     

The Damping of a Quartz Tuning Fork in Superfluid 3He-B at Low Temperatures

We have measured the damping on a quartz tuning fork in the B-phase of superfluid ³He at low temperatures, below 0.3T _c. We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid ³He-B and in superfluid ⁴He at low temperatures. In superfluid ⁴He the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid ³He the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid ³He-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid ⁴He.     

Probing Andreev Reflection in Superfluid 3He-B Using a Quartz Tuning Fork

Direct measurements of the Andreev reflection of the quasiparticles excitations in superfluid ³He-B in the ballistic regime at 0.5 bar using a quartz tuning fork are presented. Based on these measurements, we were able to determine the value of the ratio Δ(0)/kT _c to be 1.71, in reasonable agreement with previous measurements. Moreover, it seems that Andreev reflection of excitations gives a possibility to determine the value of the constant λ characterizing the velocity field profile. This value for a tuning fork was estimated to be 1.28, different from that for cylindrical wire (λ～0.95), suggesting that the anti-phase oscillatory motion and the geometry of the tuning prongs lead to an enhancement of the velocity of the superfluid flow.     

Thermal conductivity study of thin He films adsorbed in porous glasses with well controlled pore sizes

Thermal conductivity study of thin He films adsorbed in porous glasses with well controlled pore sizes^[2] is reported. The measurements are performed in a cell where a torsional oscillator monitors the superfluid density change, for the same films for comparison. Since the heat flux through the superfluid is proportional to the superfluid velocity, we discuss the possible observation of the intrinsic critical velocity v_sl = h/ml, inherent in superfluid He films in such porous systems with unit pore length l, as discussed by Minoguchi and Nagaoka^[3], which marks the velocity at which phase slippages start to occur over macroscopic scales.on leave from: Inst. Physics near Prahaon leave from: Lukin's Research Inst. Phys. Problems, Zelnograd, Moscow.     

Nonlinear dynamics in superfluid films

We have calculated the first non-linear corrections to the period shift andQ factor of a torsional oscillator containing a film of helium. To do so we have solved the Fokker Planck equation for the distribution of vortex pairs in the presence of an oscillating superfluid velocity field. The non-linear response is predicted to be proportional tov _n ² for low values of the normal fluid velocity,v _n, which is in good agreement with the experimental results of Adams and Glaberson. For temperatures above the Kosterlitz Thouless transition temperature,T _KT, the ratio of the correlation length ₊ to the diffusion length becomes important in describing the temperature dependence of the non-linear response. We predict how the non-linear response depends on this ratio in the region where the ratio is large.     

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.     

Path integral monte carlo simulations of thin4He films on a H2 surface

Atomatically thin⁴He films of up to three monolayers on molecular hydrogen (1,1,1) surfaces are studied at T = 0.5 K, using path integral Monte Carlo. We compute the binding energy of⁴He to the H₂ substrate as a function of⁴He coverage and obtain evidence of the prewetting transition. Density profiles perpendicular to the⁴He-H₂ interface are obtained, as well as the zero point motion and effective mass of⁴He parallel to the substrate surface. The superfluid density of⁴He vs. coverage is calculated, and the intermediate scattering function is computed, from which we estimate the speed of third sound. Finally, we calculate the vorticity-vorticity correlation function.     

Mobility tensor of negative ions in superfluid 3He-A

The mobility tensor of negative ions in the A phase of superfluid ³He is calculated for temperatures close to T _c . In this regime the scattering of superfluid quasiparticles from an electron bubble is practically elastic and the mobility tensor is expressed in terms of momentum transfer cross sections for an ion at rest. These generalized transport cross sections are obtained from the quasiparticle-ion scattering T-matrix, which we evaluate in terms of the normal state scattering amplitude. The p-wave pairing correlations in the intermediate states result in important interference effects among all partial waves in the scattering process, and, in addition, for the low-energy quasiparticles they lead to resonant states below the gap edge. These phenomena modify the scattering amplitude in the superfluid in an essential way and the differential quasiparticle-ion cross section is found to display strongly anisotropic, energy-dependent variations on the scale of the superfluid energy gap. We find that, in contrast to simple approximations, for low quasiparticle energies the parallel and perpendicular momentum transfer cross sections are very different from one another. Close to T _c , the calculated mobility remains rather isotropic, but at lower temperatures the anisotropy is considerably larger than predicted by simple approximations for the cross section. The computed results are compared with the available measurements.Supported in part by U.S. National Science Foundation Grants DMR78-21068 and DMR78-21069.     

Positive ion mobility in normal and superfluid 3He

The mobility of positive ions has been measured in the normal and superfluid phases of ³He at several pressures. Below 100 mK the normal phase mobility increases logarithmically with decreasing temperature down to the superfluid transition temperature T _c; it shows an anomalous jump near 100 mK. At low temperatures the drift velocity is nonlinear for electric fields exceeding 30 V/cm. In the superfluid the mobility, normalized to its value at T _c, is much less than for negative ions. We have also observed the anisotropic mobility in the A phase and the Landau critical velocity for pair-breaking in both superfluid phases.Work supported by the Academy of Finland.On leave of absence from Regensburg University, Regensburg, West Germany, supported by Deutsche Forschungsgemeinschaft.     

Soliton-Limited Superflow in 3He-A Between Parallel Plates

We have studied theoretically the flow of superfluid ³ He-A in parallel-plate geometry. The equilibrium order-parameter texture is calculated numerically in two spatial dimensions consisting of the coordinates along the flow direction and perpendicular to the plates. The calculations have been done using the hydrostatic theory in the Ginzburg-Landau region and assuming a large external magnetic field perpendicular to the plane of calculation. We have studied a uniform texture and a dipole-unlocked splay soliton as initial configurations. In the former case we find the Freedericksz transition and a helical instability with increasing flow. In the latter case we find instability in the soliton. This instability is closely related to the critical velocity in the presence of a vortex sheet. Also, the transverse NMR frequency shift at the soliton has been calculated.     

Dimensionality crossover of the4He superfluid transition in a slab geometry

The superfluid density of liquid⁴He is computed from vortex renormalization theories for the case of a slab geometry with a slab height L. With increasing temperature there is a crossover from three dimensions to two as the size of the largest vortex rings approaches L and they intersect with the walls, forming vortex pairs. The superfluid density becomes anisotropic, with the component parallel to the slab undergoing the universal Kosterlitz-Thouless jump, while the perpendicular component remains finite. The results are in agreement with both finite-size scaling and Monte-Carlo simulations.     

Recent Spin Pump Experiments on Superfluid 3He–A1

The superfluid ³He A₁ phase, containing a spin-polarized condensate allows us to explore the dynamics of superfluid spin current. In the mechano-spin effect (MSE), a mechanically applied pressure gradient and a superleak-spin filter enable one to directly boost spin polarization of ³He in a small chamber. We are developing new apparatus for achieving greater enhancement of spin density. A development of a new-type ³He-hydraulic actuator has been already reported. We present here the construction of new-type of superleak-spin-filter made of packed powder aluminum oxide (referred as PAP-SL). The PAP-SL is popular in the study of superfluid ⁴He, but has not been established for that of the superfluid ³He. The attempt to construct the PAP-SL for the spin pump experiment was made by using aluminum oxide powder with nominal 1 μm powder diameter and with packing fraction of 40 %. Before executing the experiment, the nuclear demagnetization cryostat of ISSP, Univ. Tokyo which has been used for this experimental activity, was heavily damaged by the 2011 Great East Japan (Higashi Nihon) Earthquake. The repair work and earthquake damage protection strengthening has just been accomplished.     

Depression of the superfluid transition in4He

We study superfluid⁴He near T in a homogeneous metastable state where a finite superfluid velocity v_s is present. Neglecting vortices we perform a renormalization-group calculation of the critical velocity v_sc(T) at which the superfluid state becomes unstable. We apply this result to the situation where the superfluid velocity is induced by a finite heat current Q. A critical heat current Q_c(T) corresponding to v_sc(T) is found which implies a transition temperature T (Q)=T[1–A_oQ^x]. We determine the exact exponent x=[(d–1)v] ^–1 0.744 in d=3 dimensions and calculate A_o in one-loop order. Our results for A_o and x are compared with recent experimental data.     

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.      

Acoustic Resonance of Superfluid 3He in Parallel Plates

We performed an acoustic resonance experiment of superfluid ³He confined in a stack of parallel plates, and found the fourth sound resonance. From its velocity, the superfluid density fraction was calculated. No size effect was found because the gap between parallel plates were much larger than the superfluid coherence length. The energy loss of the resonance was also measured. We found that the hydrodynamic theory qualitatively described its temperature dependence, but it could not describe the gap width dependence. Possible explanations is discussed in the text. More over, we found the unidentified resonance that cannot be explained by conventional sound modes.     

Manipulation of \hat l Texture by Counterflow in Superfluid 3He A1

A rectangular resonator chamber is fitted with three pairs of second sound transducers for studying the spin-entropy wave propagation in ³ He A ₁. The anisotropy in the spin-entropy wave propagation velocity is unambiguously established by simultaneously measuring the modes propagating in both parallel and perpendicular directions to the applied magnetic field. The anisotropic texture within the cell is manipulated by introducing oscillatory counterflows with one transducer. The manipulated texture is monitored by measuring the resonant mode with the pair of transducers which are orthogonal to the drive transducer. The manner of texture manipulation depends on both the amplitude and frequency of the drive. In some cases, the observed changes in texture are abrupt and hysteretic. The texture transitions may be of first order.