Zero-sound attenuation in rotating and stationary3He-A and3He-B

We report on measurements of zero-sound attenuation in rotating and stationary³He-A and³He-B, in magnetic fields up to 350 mT. Strong and highly nonlinear rotation speed dependencies of sound amplitudes have been observed in both phases. The data gives information on vortex types and core sizes, although the analysis is not straightforward. The anomalous attenuation in³He-B at 200 mT near the AB transition, both in the stationary and in the rotating state, is interpreted to arise from the distortion of the energy gap of the B phase. Excess attenuation during the AB phase change was observed. Evidence for soft vortex cores in³He-B is presented. In addition, a critical velocity in the vortex free state, related to a textural transition, and the vortex creation times have been measured in³He-B. Furthermore, a metastable structure, possibly a new vortex state, has been observed in³He-B by rotating the sample through the A B transition.     

Acoustic attenuation in superfluid3He-B at low pressures

The attenuation of zero sound in superfluid³He-B has been measured up to 160 cm^–1, at pressures less than 4 bar and at frequencies 34.2, 44.2, and 54.0 MHz. The contribution of pair breaking to the attenuation has been measured for the first time. The gap (J=1 ^–) mode has been studied in magnetic fields up to 80 mT and the structure of its Zeeman components revealed. Coupling to the gap mode in the applied field allows a direct spectroscopic measurement of the energy gap. In zero magnetic field, the attenuation is well described by the theory of Wölfle, showing agreement with the magnitude of the attenuation and the frequency of the squashing mode resonance, for an appropriate choice of the parameterz=(c ₀–c₁)/c₁, wherec ₀, c₁ are the velocities of zero and first sound. This provides a determination of the Landau parameterF ₂ ^s and indicates that thef-wave interaction is negligible at these low pressures.     

Orbital Viscosity in Superfluid 3He-B in a Magnetic Field

No Heading Orbital viscosity is usually associated with the A phase of superfluid ³He which has a finite orbital angular momentum even in zero magnetic field. The B phase has no orbital angular momentum in zero magnetic field, but both spin and orbital angular momenta are induced by a field. The Leggett equations for spin dynamics assume that the orbital angular momentum can only charge on timescales much longer than those involved in spin dynamics. We calculate the orbital viscosity of the B phase in both the hydrodynamic and ballistic limits. At low temperatures the orbital viscosity becomes vanishingly small which gives rise to the possibility of coupled spin-orbit dynamics.PACS numbers: 67.57.Hi, 67.57.Lm     

Optical interferometry in superfluid3He-B

We report interferometric measurements on 0.1 ... 1 mm thick films of superfluid ³He-B. The menisci of three different rotational states of the superfluid were observed and analyzed theoretically using two-fluid hydrodynamics: These are (i) the equilibrium vortex state in which the superfluid and the normal components corotate (solid body rotation), (ii) the vortex-free state (the Landau state), in which only the normal component rotates, and (iii) the quasistationary vortex state in which only the superfluid fraction rotates (pure superfluid rotation). The Landau state manifested itself by a reduced parabolic meniscus at rotation speeds below the critical angular velocity 0.2 rad/s for vortex formation. Transition from the Landau state to the equilibrium vortex state yielded a sudden deepening of the meniscus when _c was exceeded. After a rapid halt of the cryostat, we observed a novel meniscus which was produced by the superfluid rotation while the normal component was at rest. The enhanced depth of this meniscus is governed by the reactive mutual friction parameter B'.By employing laser light, both for imaging and for thermomechanical excitation, we measured the response of a thin superfluid layer to a heat pulse and analyzed it within the theory of two-fluid hydrodynamics. The data were employed, using the dispersion relation for thin film oscillations, to deduce the second viscosity coefficient ₃ close to T_c.     

Electron-electron scattering and ultrasonic attenuation in potassium

The electron-electron scattering contribution to the ultrasonic attenuation in potassium at low temperatures is evaluated using the Landau Fermi liquid theory. The scattering function is evaluated using the approximation suggested by MacDonald and Geldart. The results are compared with theoretically evaluated electron-phonon scattering contributions. The results show that the electron-electron scattering contribution is of the same order as the electron-phonon scattering contribution in the 2–5 K range. Below 2 K the electron-electron scattering predominates.     

Domain Walls in Superfluid 3He-B

No Heading We consider domain walls between regions of superfluid ³He-B in which one component of the order parameter has the opposite sign in the two regions far from one another. We report calculations of the order parameter profile and the free energy for two types of domain wall, and discuss how these structures are relevant to superfluid ³He confined between two surfaces.PACS numbers: 67.57.Np     

Transverse waves in superfluid3He-B

We examine the theory of collisionless transverse current waves in bulk superfluid³He-B, including the coupling to the order parameter collective modes. At low frequencies, Ω ≪ δ(T), the order parameter modes do not contribute to the restoring force for a transverse current, and the quasiparticle contribution drops rapidly as the gap in the spectrum develops. Thus, low-frequency transverse sound becomes overdamped at temperatures nearT _c . However, at low temperatures (T ≲0.3T _c ) the off-resonant coupling to the J = 2⁻,M = +-1 modes stabilizes a propagating transverse current mode, with a large phase velocity and low damping for frequencies above a critical frequency that is approximately that of theJ = 2 ⁻ mode. We also discuss the similarities and differences of longitudinal and transverse sound in the superfluid phases. For example, in zero field, right- and left-circularly polarized waves are degenerate. A magnetic field, with , lifts this degeneracy, giving rise to the analog of circular dichroism and birefringence of electromagnetic waves. Thus, transverse waves may be more easily detected in the B-phase than in normal³He.     

Coherent Spin Precession in Superfluid 3He-B Excited in a Field Minimum at Low Temperatures

No Heading The persistent precessing domain (PPD) is an isolated region of coherent spin precession which is observed in the B phase of superfluid ³He at the lowest achievable temperatures. It has many unusual properties and its free decay can exceed 1000s at the lowest temperatures. Previous observations of the PPD were highly irreproducible but we now find the PPD to be very reproducible when there is a field minimum along the cell axis. Here we discuss measurements of the PPD as we control the magnetic field profile, allowing the depth of the minimum to be adjusted.PACS numbers: 67.57.Lm, 67.57.Jj, 67.57.Fg     

Textural singularities in superfluid3He-B

The absorption signal occasionally found missing in the middle of resonance absorption lines in NMR is explained on the basis of a textural singularity of the anisotropy axis in the B phase of ³ He. The singularity combines with the field gradient present to give rise to an asymmetric hole in the signal with a singularity on the high-frequency side. The line shapes and temperature dependence are predicted and agree well with experiment. Spin waves are found to be trapped by the potential well formed by the texture and the field gradient. The frequency intervals predicted for the spin waves also agree well with experiment.Work supported in part by National Science Foundation Grant No. NSF DMR 74-18030.     

Three-dimensional ultrasonic reflection and attenuation imaging

A three-dimensional, volumetric, data acquisition and reconstruction system for ultrasonic imaging is described. The method entails storing the digitized waveforms from each element of a multielement annular array, with bidirectional mechanical scanning. The system was implemented through digitization of the RF signals from each of the rings of an annular-array transducer, storage of the signals in computer memory, and offline image reconstruction. Initial reflection and reflex transmission images acquired with this system are presented. The results of different image reconstruction algorithms are demonstrated.     

Transverse zero sound in superfluid3He-B

The dispersion of the transverse zero sound in superfluid³He-B in the colisionless limit is studied theoretically. The dispersion is most easily understood as due to strong coupling between two distinct modes; the original zero-sound mode which is present in normal liquid and the collective mode with energy gap _t (T) proportional to (T), the temperature-dependent energy gap.Work supported by the National Science Foundation.     

Dislocation damping and the ultrasonic attenuation in tin

Measurement of ultrasonic attenuation in single crystals of pure tin has been taken at 300 K for frequencies varying from 3 to 50 MHz and at different dislocation densities. There is a resonant behaviour in attenuation due to dislocation and the resonance frequency v_o increases with an increase in dislocation density A. Experimentally it has been observed that there is a linear variation between lnΛ and $\text{v}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. A systematic broadening of the resonance curve takes place with increasing dislocation density. The broadening of the resonance curve has been explained as being due to damping by mutual interaction between the dislocations. An estimate of dislocation damping has been made at different dislocation densities. The total damping due to phonons and electrons has also been estimated at 300K and 77 K.     

Measurement of Turbulence in Superfluid 3He-B

The experimental investigation of superfluid turbulence in ³He-B is generally not possible with the techniques which have been developed for ⁴He-II. We describe a new method by which a transient burst of turbulent vortex expansion can be generated in ³He-B. It is based on the injection of a few vortex loops into rotating vortex-free flow. The time-dependent evolution of the quantized vorticity is then monitored with NMR spectroscopy. Using these techniques the transition between regular (i.e. vortex number conserving) and turbulent vortex dynamics can be recorded at T ～ 0.6 T_c and a number of other characteristics of turbulence can be followed down to a temperature of T ? 0.4 T_c. PACS numbers: 47.37, 67.40, 67.57.     

Thermal behavior of quasiparticles in3He-B

We describe experiments on the transport of heat within a cell cooled by nuclear demagnetization of copper and containing³He-B at temperatures between 0.1 and 0.4 T_C. Within the bulk liquid helium, heat is transported by ballistic quasiparticles. In this case the conventional concept of boundary resistance is not applicable to the analysis of the heat exchange between refrigerant and³He. Rather, the cell geometry plays the important role. A thermal breakthrough in the cell is observed under conditions of heat flow large enough that the spin-lattice Korringa link to the copper refrigerant nuclei becomes saturated. At this point the lattice temperature rises, allowing heat to be transferred rapidly around the cell within the copper lattice, short-circuiting the liquid helium. We develop a simple model of heat transfer by ballistic quasiparticles which describes well the principal experimental features.     

Experiments on nonlinear acoustics in3He-B

Observations and applications of nonlinear acoustic phenomena in superfluid³He-B are reported. Two-phonon absorption (TPA) by the real squashing (rsq) mode has been detected under several experimental conditions below p = 3.5 bar, using two coincident sound pulses. The attenuation peak height has been investigated as a function of the energy densities of the two sound waves. We discovered the five-fold Zeeman splitting of TPA by parallel sound pulses in an applied magnetic field and the two-fold dispersion splitting due to the finite wave vector of the mode when the two sound pulses are mutually perpendicular. The dispersion relation of the real squashing mode has been investigated at zero pressure and in zero magnetic field by exciting the mode with two parallel, perpendicular, or antiparallel sound waves. Experimental values for the parameters that determine the collective-mode velocities have been extracted from the positions of the observed attenuation maxima. An anomalous structure has been observed in the attenuation and phase velocity spectra of a single high-intensity sound wave near the threshold for pair breaking by two phonons; in an applied magnetic field the phase velocity anomaly splits into a triplet.     

The reverse AC-Josephson effect in 3He-B

No Heading We have investigated ³He Josephson currents under an externally applied ac-pressure modulation. The ³He-flow was driven by the motion of a flexible membrane through an array of 65 by 65 holes of 150 nm size in a 50 nm thick SiN wall. The membrane was deflected electrostatically. If a sinusoidal modulated electrostatic force was applied to the membrane, we could observe phase locking of the Josephson oscillations to the external ac-drive. As a result, a zero net flow through the weak link was observed while the membrane was stuck for many seconds at a non zero pressure position. For this pressure the Josephson frequency matched the ac-drive frequency. We could resolve the dynamics which led to this trapped, phase locked state. The dynamics looked quite similar to dynamics which took place when the system ended up in Helmholtz oscillations at the zero pressure difference equilibrium state.PACS numbers: 67.57.De, 67.57.Fg, 74.50.+r, 85.25.Cp     

High Frequency Sound in Superfluid 3He-B

We present measurements of the absolute phase velocity of transverse and longitudinal sound in superfluid ³He-B at low temperature, extending from the imaginary squashing mode to near pair-breaking. Changes in the transverse phase velocity near pair-breaking have been explained in terms of an order parameter collective mode that arises from f-wave pairing interactions, the so-called J=4^? mode. Using these measurements, we establish lower bounds on the energy gap in the B-phase. Measurement of attenuation of longitudinal sound at low temperature and energies far above the pair-breaking threshold, are in agreement with the lower bounds set on pair-breaking. Finally, we discuss our estimations for the strength of the f-wave pairing interactions and the Fermi liquid parameter, F ₄ ^s .     

Quasiclassical theory of vortices in3He-B

We report weak-coupling numerical calculations of the order parameter and the free energy of isolated vortices in superfluid³He in the framework of the quasiclassical theory of superfluid Fermi-liquids. Unlike earlier work with the Ginzburg-Landau theory, our results are not restricted to the vicinity ofT _c. We show that Fermi-liquid effects play an important role at lower temperatures. It appears there is a transition from the double core vortex to an A-phase-core vortex at the vapor pressure just above 0.5T_c.     

Dynamic Remanent Vortices in Superfluid 3He-B

We investigate the decay of vortices in a rotating cylindrical sample of ³He-B, after rotation has been stopped. With decreasing temperature vortex annihilation slows down as the damping in vortex motion, the mutual friction dissipation α(T), decreases almost exponentially. Remanent vortices then survive for increasingly long periods, while they move towards annihilation in zero applied flow. After a waiting period Δt at zero flow, rotation is reapplied and the remnants evolve to rectilinear vortices. By counting these lines, we measure at temperatures above the transition to turbulence ∼0.6 T _c the number of remnants as a function of α(T) and Δt. At temperatures below the transition to turbulence T≲0.55 T _c, remnants expanding in applied flow become unstable and generate in a turbulent burst the equilibrium number of vortices. Here we measure the onset temperature T _on of turbulence as a function of Δt, applied flow velocity v=v _n−v _s, and length of sample L.