Andreev Reflection of Quasiparticles by a Vortex Tangle in Superfluid 3He-B?

We have made the surprising discovery that the thermal damping of a vibrating wire resonator in superfluid ³ He-B at ultra low temperatures is considerably depressed when a second wire in the vicinity is driven supercritically. The damping of a vibrating wire resonator at low velocities in the B-phase arises from the scattering of quasiparticle excitations and has a temperature dependence proportional to the Boltzmann factor exp(–/kT) at low temperatures. At higher velocities (v>v_L/3), the wire breaks Cooper pairs and emits a quasiparticle beam. At first sight it seems paradoxical that heating the superfluid can reduce the quasiparticle flux on a neighbouring wire. We can only understand this on the basis that vorticity emitted by the supercritical wire shields, via Andreev reflection, part of the background quasiparticle flux from reaching the other wire. If this interpretation is correct, these techniques will provide a sensitive probe of vortex dynamics in the ultra low temperature regime.     

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.     

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.     

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.      

Thermodynamic Potential for Superfluid 3He in?Aerogel

We present a free energy functional for superfluid ³He in the presence of homogeneously distributed impurity disorder which extends the Ginzburg-Landau free energy functional to all temperatures. We use the new free energy functional to calculate the thermodynamic potential, entropy, heat capacity and density of states for the B-phase of superfluid ³He in homogeneous, isotropic aerogel.     

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.     

3He in Aerogel – an Inhomogeneously Disordered Unconventional Superfluid

We have examined the superfluidity of ³ He in 98.2% porous silica aerogel with up to 34% ⁴ He at 21.6 bar. The mixture is phase-separated for ⁴ He fractions between 11% and 34%. The ⁴ He-rich, phase preferentially occupies the regions of highest silica density in the aerogel, thus modifying the distribution of the correlated disorder seen by superftuid ³ He. The ³ He T _c increases slightly with ⁴ He content while the superfluid fraction decreases rapidly. This behavior is inconsistent with that of ³ He in a homogeneously scattering medium and is analogous to that of a granular superconductor.     

Bose-Einstein Condensation of Magnons in Superfluid 3He

The possibility of Bose-Einstein condensation of excitations has been discussed for a long time. The phenomenon of the 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 has 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 a mode of the coherent precession in compressed aerogel. The coherent precession has been also found in ³He-A in compressed aerogel. Here we demonstrate that all these cases are examples of a Bose-Einstein condensation of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by different types of spin-orbit coupling in the background of the coherent precession.      

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).     

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.     

Transition to Turbulence and Critical Velocity in Superfluid Solution of 3He in 4He

By the method of oscillating tuning fork, we carried out researches of the transition to turbulence in superfluid solution of 5% ³He in ⁴He at temperatures of 100 mK–300 mK. The critical velocity υ _c of the turbulence appearance is determined through measuring the volt-ampere characteristics. It is established that in the mixture the temperature dependence of the critical velocity is non-monotonous and differs strongly from that in pure ⁴He. Unlike ⁴He, the step-like anomalies on resonance curves were observed which, presumably, is connected with instability of the vortex system under the conditions where the core of the vortex is filled by the atoms of ³He. It is shown that such anomalies appear at the temperatures below 0.9 K, at the same time at temperatures below ～0.5 K they appear even at υ<υ _c .     

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.     

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.     

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.     

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.     

Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid ⁴He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution “turbulent drag”. The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.     

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.     

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.     

Coupled Dynamics for Superfluid $$^4\hbox {He}$$ in a Channel

We study the coupled dynamics of normal and superfluid components of superfluid \(^4\hbox {He}\) in a channel considering the counterflow turbulence with laminar normal component. In particular, we calculated profiles of the normal velocity, the mutual friction, the vortex line density and other flow properties and compared them to the case where the dynamic of the normal component is “frozen.” We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore, coupling becomes stronger. The commonly measured flow properties also change when the coupling between the two components is taken into account.