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.     

Developed Capillary Turbulence on the Surface of Normal and Superfluid 4He

The capillary turbulence on the surface of normal and superfluid liquid ⁴He has been studied experimentally. It is observed for the first time that the value of the high-frequency boundary ω _b of the inertial interval increases significantly when liquid helium transits from normal to superfluid state, and that in superfluid He-II the correlation function of the surface deviation from equilibrium state in frequency representation can be described well by a power dependence with the index m close to −4.3.      

Numerical Simulations of Superfluid Turbulence under Periodic Conditions

This paper is devoted to numerical simulation of vortex tangle dynamics in superfluid helium. The problem is solved on the base of the so called reconnection ansatz consisting of the equation of motion for vortex lines plus reconnection of a loop. A new algorithm, which is based on consideration of crossing lines, is used for the reconnection processes. Calculations are performed for a cubic box. Periodic boundary conditions are applied in all directions. We use the 4th order Runge-Kutta method for the integrations in time. The dynamics of quantized vortices with various counterflow velocities is studied. The density of vortex lines and number of reconnections as functions of vortex line density are calculated.      

Electrostatic Manipulation of Level of Bulk Liquid for Studies of Saturated Superfluid 3He Films

In studies of saturated superfluid helium films, the level of bulk liquid is an important parameter in determining the thickness of the film. To change the level at low temperatures, a complicated system with a bellows and an extra fill line is usually needed. In this paper, we report a simple device that can be used to change the level using an electrostatic force. This level controller consists of a stack of 60 silver plates of 0.1 mm thickness, separated from each other by a 0.1 mm gap. The application of a dc voltage V to every other plate pulls the dielectric liquid ³He into the gaps, resulting in the drop of the bulk level. The change in level is in agreement with that expected by the balance between the electrostatic force and gravity, and the decrease is as large as 0.27 mm at V=200 V. The level controller is also used to detect the superfluid transition of bulk liquid ³He through the sudden reduction of the response time after V is varied.     

The Dynamics of Vortex Generation in Superfluid 3He-B

A profound change occurs in the stability of quantized vortices in externally applied flow of superfluid ³He-B at temperatures ?0.6?T _c, owing to the rapidly decreasing damping in vortex motion with decreasing temperature. At low damping an evolving vortex may become unstable and generate a new independent vortex loop. This single-vortex instability is the generic precursor of turbulence. We investigate the instability with non-invasive NMR measurements on a rotating cylindrical sample in the intermediate temperature regime (0.3–0.6)?T _c. From comparisons with numerical calculations we interpret that the instability occurs at the container wall, when the vortex end moves along the wall in applied flow.     

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.     

Charged Tangles of Quantized Vortices in Superfluid 4He

We show that turbulence in superfluid ⁴He at low temperatures can be generated and probed by injected ions trapped on vortex cores. The results of our recent experiments, in which negative ions were injected during short and long periods, in different quantities, and into different applied electric fields, are outlined. Three very different mechanisms of vortex-assisted transport of trapped ions were observed: one is on isolated vortex rings while two others are associated with tangles of vortex lines. It seems there are two different types of vortex tangles that can be characterized by the velocity of ion motion through them: a drifting polarized tangle in a low-dissipation state that mainly advects trapped ions, and a more isotropic tangle in a highly-dissipative state, sustained by a continuous forcing by the ion current in an applied electric field, through which trapped ions move rapidly.     

Accurate Density Response Function of Superfluid 4He at Freezing Pressure: Is DFT Successful for Superfluid Freezing?

An accurate density response function ??(q) of superfluid ⁴He at zero temperature and at freezing pressure, up to about q=8 Å^?1, has been obtained via dynamic structure factors, S(q,??), extracted from imaginary time density?Cdensity correlation functions computed with an exact Path Integral projector method. A new statistical approach (Vitali et al. in Phys. Rev. B 82:174510, 2010) to inverse problems has been used to extract S(q,??); contrarily to analogous ??analytic continuation?? approaches, this new method has been found able to separate a well defined elementary excitation peak from multi?Cphonon contributions. We have applied density functional theory (DFT) to a superfluid?Csolid transition with the obtained ??(q). With this accurate input, DFT gives unphysically unstable superfluid against solidification which is consistent with conventional works. We discuss the possible defect of DFT.     

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).     

Dispersion-Induced Splitting of the Collective Mode Spectrum in Axial and Planar Phases of Superfluid 3He

The whole collective mode spectrum in axial and planar phases of superfluid ³He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k‖l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k ⊥ l. In planar 2D-phase, which exists in the magnetic field (at H>H _C ) we find that for clapping modes the degeneracy depends on the direction of the collective mode momentum k with respect to the external magnetic field H, namely: the mode degeneracy remains the same as in case of zero momentum k for k‖H only. For any other directions different from this one (for example, for k ⊥ H) there is twofold splitting of these modes. The obtained results imply that new interesting features can be observed in ultrasound experiments in axial and planar phases: the change of the number of peaks in ultrasound absorption into clapping mode. One peak, observed for these modes by Ling et al. (J. Low Temp. Phys. 78:187, 1990), will split into two peaks in a planar phase and into three peaks in an axial phase under the change of ultrasound direction with respect to the external magnetic field H in a planar phase and with respect to the vector l in an axial phase. In planar phase, some Goldstone modes in the magnetic field become massive (quasi-Goldstone) and have a similar twofold splitting under the change of ultrasound direction with respect to the external magnetic field H. The obtained results as well will be useful under interpretation of the ultrasound experiments in axial and planar phases of superfluid ³He.     

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 .     

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.     

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.     

Density Variation of the Frustrated Ferromagnetism in 2D Solid 3He

We measured heat capacities of the second layer incommensurate (IC) solid ³He adsorbed on graphite preplated with monolayer ⁴He (³He/⁴He/gr) in a wide temperature range (0.3 ≤T≤ 80 mK). From the high temperature series expansion fitting, we obtained density dependences of the multiple spin exchange interactions inherent to this two-dimensional quantum solid. Compared with the earlier results for the ³He/³He/gr system, the magnitude of the effective two-spin exchange interaction is clearly smaller at the lowest densities, while it is nearly the same at the highest densities. We argue that this difference is caused by the different densities of the second layer IC solids in the two systems. We also show that the total spin-entropy changes deduced from the present heat capacity data are smaller than the expected value by about 18%.     

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.     

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.     

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.     

Instability of Quantized Vortices Attached to Oscillating Boundaries in Superfluid 4He

The motion of quantized vortices is studied using a vibrating wire in superfluid ⁴He. A vortex filtering method provides a superfluid practically free of remanent vortices in which the vibration of a wire cannot generate turbulence. Vortex lines are produced by cooling through the superfluid transition and remain forming bridges between a wire and a surrounding wall. Bridged remanent vortices increase the resonance frequency of a vibrating wire: the rate of an increase due to the remanent vortices is constant in a laminar flow regime and steeply increases in a turbulent flow regime with increasing wire velocity. These results suggest that oscillation of the bridged vortices provides a linear contribution to the wire vibration in the laminar flow regime, until instability occurs in the oscillation of the vortices, causing turbulence.      

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.