Textures of Rotating Superfluid 3He–A in a Single Narrow Cylinder

We have studied textures of the rotating superfluid ³He–A in a single narrow cylinder by NMR measurement. In a narrow cylinder, the characteristic textures such as Mermin-Ho texture (Mermin and Ho in Phys. Rev. Lett. 36:594, 1976) can be formed in order to minimize the free energy of the system determined by the effect of the wall, the magnetic field, the dipole interaction, the flow of the superfluid and so on. We observed three types of NMR absorption spectra dependent on the processes used to form A-phase in a narrow cylinder. A particular texture shows a characteristic spectrum and we can determine the texture from the observed spectrum by comparing the resonance frequency of the peak in NMR spectrum with the calculated one of the spin wave mode. We present the identification and the phase diagram of textures of the rotating superfluid ³He–A in a single narrow cylinder.     

Phase Transitions of Superfluid 3He in 0.8-μm Slab Geometry

We have studied superfluid ³ He in 0.8 m slab geometry by cw-NMR method. The static magnetic field for NMR was 22 mT and was perpendicularly applied to the surface. At pressures from 5 bar to 27 bar, we observed the negative shifts of NMR frequencies below the transition temperatures. Moreover we observed the fast order phase transition with the supercooling phenomena at lower temperatures, but NMR frequencies did not show a jump as they do at the A-B transition in the bulk liquid. Although the phase at low temperatures seemed to be B-phase, NMR frequencies still had the negative shifts.     

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.     

Specific Heat Near the Superfluid Transition of a 0.9869 μm 4He Film

We report measurements of the specific heat of ⁴He near the superfluid transition while confined between silicon wafers at 0.9869 m separation. These data are analyzed to check on the behavior expected from correlation-length scaling. Comparison is also made with other data for planar confinement, as well as data for cylindrical confinement. These represent different lower-dimensional crossovers. We find that the present data scale very well above the bulk transition temperature, and in the region immediately below it. Near the specific heat maximum however, the data for planar confinement do not collapse on a universal curve. We compare these results with specific theoretical scaling functions. In particular we find that on the normal side, and for large enough values of the scaling variable, one can describe the data well using the concept of the surface specific heat. The locus of the data in this region agrees well with the most recent theoretical calculations.     

Convective Turbulence in Superfluid Solutions 3He–4He

In present work, we continue our experimental investigations of heat instability in superfluid ³He–⁴He solutions heated from below. We research two solutions with ³He concentrations 5.0% and 9.5% for temperature of 270 mK. It is found that for 5% solution the dependence is linear in temperature range studied whereas for the solution of 9.5% we observed the deviation from linear dependence above some critical value . This effect manifests the thermal instability which appears under start of phase separation in 9.5% solution if heat flow is switched on. For 5.0% solution where one does not observe the phase separation at the values of applied, the instability was not observed. To identify the possible mechanism of a thermal instability in stratified solution, we estimated the dependence of the Nusselt number on relative Raileigh number Ra/Ra _c . One observes that the dependence can be fitted as Nu=(Ra/Ra _c ) ^b where b=0.31±0.04. Note that the dependence obtained agrees rather good with the empiric expression of (Busse in Rep. Prog. Phys. 41:1929, 1978) and connecting the numbers Nu and Ra for turbulent convection. This gives grounds to conclude the heat transfer in a stratified solution is realized by transition to the regime of turbulent convection.      

Orbital Damping of the Oscillating Superfluid ^3He A–B Interface at Low Temperatures

We present a model for the friction and effective mass of an oscillating superfluid $^3$ He A–B interface due to orbital viscosity in the B-phase texture close to the interface. The model is applied to an experiment in which the A–B interface was stabilised in a magnetic field gradient at the transition field $B_c = 340$  mT at 0 bar pressure and at a very low temperature $T \approx 0.155$  mK. The interface was then oscillated by applying a small additional field at frequencies in the range 0.1–100 Hz. The response of the interface is governed by friction and by its effective mass. The measured dissipation does not fit theoretical predictions based either on the Andreev scattering of thermal quasiparticles or by pair-breaking from the moving interface. We describe a new mechanism based on the redistribution of thermal quasiparticle excitations in the B-phase texture engendered by the moving interface. This gives rise to friction via orbital viscosity and generates a significant effective mass of the interface. We have incorporated this mechanism into a simple preliminary model which provides reasonable agreement with the measured behaviour.     

Transport in 3He–4He Mixtures in Restricted Geometry

The effect of wall scattering on transport in dilute degenerate ³He–⁴He mixtures in quasi-2D flow channels or films is discussed. The calculation of the quasiparticle mean free path combines particle–wall and particle–particle collisions including the interference between them. The spin polarization affects the wall-driven contribution by changing bulk mean free path and particle wavelength. The expressions for the wall contribution to transport coefficients are especially transparent in the limiting cases of large and small bulk mean free paths. The calculated temperature, concentration, and polarization dependences of the transport coefficients allow one to extract parameters of surface roughness from experimental data on transport.     

Specific Heat and Superfluid Density of 4He near T λ of a 33.6 nm Film Formed Between Si Wafers

We report measurements of superfluid density and specific heat of a 33.6 nm film near the superfluid transition. The film is formed between two patterned and directly bonded silicon wafers. These measurements were undertaken with the primary purpose of understanding coupling and proximity effects in a situation when the film was in contact with helium in a larger confinement (Perron et al. in Nat. Phys. 6:499, 2010; Perron and Gasparini in Phys. Rev. Lett. 109:035302, 2012). However, these data are also relevant to issues of correlation-length finite-size scaling. This is the thinnest hard-wall confined film for which such scaling has been tested for the specific heat and superfluid density. One expects that at some small thickness such scaling should fail. We compare our results with previous data of helium in a similar confinement but at larger thickness. We find good agreement with scaling in regions where previous data scaled, and confirm the lack of scaling where previously reported. In our analysis we consider a native oxide growth between the etching and bonding steps of cell fabrication and its effect on our scaling analysis.     

Texture and Vortex of Rotating Superfluid 3He-A in Parallel-plate Geometry

Unique types of textures and vortices of superfluid ³He in restricted geometries have been discussed. We investigated cw-NMR in rotating ³He A-phase in parallel plate geometries with gaps of 12.5 μm at 3.05 MPa. We observed a very sharp spectrum at rest which had shifted negatively as f=f _L?0.93f _A(T), where f _A(T) is the full transverse dipole shift in A-phase. The large negative shift of 0.93f _A(T) indicates that l ⊥ d. When we rotated the sample with rotation speed Ω faster than the critical Ω _Fr, a new satellite signal appeared nearly at f _L. The satellite signal intensity increased with increasing Ω, reached a maximum at Ω _c and slowly decreased up to the maximum Ω of 2π rad/s. When Ω decreased from the maximum speed, the satellite signal rapidly decreased and disappeared at 5.5 rad/s down to zero rad/s. We measured the temperature dependence of the satellite signal intensity, Ω _Fr and Ω _c. We propose a model for the satellite signal, which is attributed to spin wave in Fréedericksz transition region induced by the counter flow. We also compare the satellite signal with Kee and Maki’s bound pair of HQV.     

Superfluid 3He Confined in a Single 0.6 Micron Slab

We present the preliminary results of our studies of superfluid ³He in a 0.6 μm thick slab using NMR. Below T _c the A phase is observed, and at low pressures the region of stability of the A phase extends down to the lowest temperatures reached, as described elsewhere. At pressures above 3.2 bar another, so far unidentified phase is observed at low temperatures. In this article we focus on the behavior of this phase and the transition between this phase and the A phase, all studied at 5.5 bar. The NMR response at low temperatures exhibits two possible frequency shifts and the transition is hysteretic in temperature.     

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.     

Proximity Effect between a Dirty Fermi Liquid and Superfluid 3He

The proximity effect in superfluid ³He partly filled with high porosity aerogel is discussed. This system can be regarded as a dirty Fermi liquid/spin-triplet p-wave superfluid junction. Our attention is mainly paid to the case when the dirty layer is in the normal state owing to the impurity pair-breaking effect by the aerogel. We use the quasiclassical Green’s function to determine self-consistently the spatial variations of the p-wave order parameter and the impurity self-energy. On the basis of the fully self-consistent calculation, we analyze the spatial dependence of the pair function (anomalous Green’s function). The spin-triplet pair function has in general even-frequency odd-parity and odd-frequency even-parity components. We show that the admixture of the even- and odd-frequency pairs occurs near the aerogel/superfluid ³He-B interface. Among those Cooper pairs, only the odd-frequency s-wave pair can penetrate deep into the aerogel layer. As a result, the proximity-induced superfluidity in a thick aerogel layer is dominated by the Cooper pair with the odd-frequency s-wave symmetry. We also analyze the local density of states and show that it has a characteristic zero-energy peak reflecting the existence of the odd-frequency s-wave pair, in agreement with previous works using the Usadel equation.     

Microkelvin Thermometry with Bose–Einstein Condensates of Magnons and Applications to Studies of the AB Interface in Superfluid ^3He

Coherent precession of trapped Bose–Einstein condensates of magnons is a sensitive probe for magnetic relaxation processes in superfluid $^3$ He-B down to the lowest achievable temperatures. We use the dependence of the relaxation rate on the density of thermal quasiparticles to implement thermometry in $^3$ He-B at temperatures below $300\,\upmu $ K. Unlike popular vibrating wire or quartz tuning fork based thermometers, magnon condensates allow for contactless temperature measurement and make possible an independent in situ determination of the residual zero-temperature relaxation provided by the radiation damping. We use this magnon-condensate-based thermometry to study the thermal impedance of the interface between A and B phases of superfluid $^3$ He. The magnon condensate is also a sensitive probe of the orbital order-parameter texture. This has allowed us to observe for the first time the non-thermal signature of the annihilation of two AB interfaces.     

Formation of a Mesa Shaped Phonon Pulse in Superfluid 4He

We present a theory for the formation of a mesa shaped phonon pulse in superfluid ⁴He. Starting from the hydrodynamic equations of superfluid helium, we obtain the system of equations which describe the evolution of strongly anisotropic phonon systems. Such systems can be created experimentally. The solution of the equations are simple waves, which correspond to second sound in the moving phonon pulse. Using these exact solutions, we describe the expansion of phonon pulses in superfluid helium at zero temperature. This theory gives an explanation for the mesa shape observed in the measured phonon angular distributions. Almost all dependencies of the mesa shape on the system parameters can be qualitatively understood.     

Transverse Acoustic Impedance Measurements for Surface States of Superfluid 3He A1 and A2 Phases

We measured the complex transverse acoustic impedance in both superfluid ³He A₁ and A₂ phases. This impedance is sensitive to surface states. In our preliminary results, the temperature dependence of the impedance in the A₁ phase is similar to that in A phase, and the imaginary part shows an anomaly in the A₂ phase. These anomalies occurred at the temperature defined as T _k , which is lower as the frequency gets higher. The similar frequency dependence of T _k in each phase suggests that the anomaly is attributed to the same origin. The frequency dependence of the T _k /T _c indicates that the shape of the surface density of each spin pair state did not greatly change in the present experimental temperature range.     

Majorana Edge Modes of Superfluid 3He A-?and?B-Phases

Motivated by a recent experiment on the superfluid ³He confined in a thin slab, we discuss the Majorana edge modes under the experimental situation. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several observables, such as local density of states, mass current for the A-phase, and spin current for the B-phase. On the basis of the quantitative calculation, we propose several experiments to check the existence of the Majorana modes.     

Spin Fluctuations in A-like Superfluid Phase of 3He in Aerogel

The frequency spectrum of the spin fluctuations δ S(t) superimposed on the coherently precessing spin modes in the A-like superfluid phase in aerogel is analysed. It is shown that the low amplitude spin fluctuations could be most easily observed in the case of an uni-axially deformed aerogel. It is demonstrated, in particular, that for axially stretched (radially squeezed) aerogel described by the U(1)LIM model the fourth order harmonic in δ S _z (t) is erased, in contrast with what is expected for the long range Leggett orbital configuration in the ³He-A (ABM state).     

3He Correlation Energy in the Random Phase Approximation: the One-Ripplon-Exchange Potential in Thin 3He–4He Superfluid Films

A new approach to the calculation of correlation energies in the random phase approximation (RPA) is introduced. The method is applied to the system of adsorbed ³ He in thin ⁴ He superfluid films. The ³ He component interacts by means of the exchange of virtual surface interactions (ripplons) in addition to the usual atom-atom interaction. We report on a calculation of the RPA contribution to the ³ He ground-state energy of a previously introduced model for this effective interaction called the one-ripplon-exchange potential (OREP). V_OREP is manifestly frequency dependent and complex. In this paper we study the differences in the RPA contribution to the ground-state energy between the fully complex and frequency dependent V_OREP and V_OREP in the real, static limit.