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.     

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.     

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.     

Spin-independent transport parameters for superfluid3He-B

The scalar kinetic equation for Bogoliubov quasiparticles in the B phase of superfluid³He is discussed and the collision integral is represented in a compact form. For the cases of shear and second viscosity and diffusive thermal conductivity the problem is reduced to solving one-dimensional integral equations. The quasiparticle interaction enters via weighted angular averages of the normal state scattering amplitude. The effect of strong coupling renormalization of the gap function is accounted for. The transport coefficients are exactly related to relaxation parameters that describe how the system tends toward local equilibrium. For low temperatures the transport parameters are evaluated exactly, including corrections of orderT/T _c. The results are compared with those of a previous paper in which an approximate form of the collision operator was used, as well as with results of a variational approach and with recent experimental data.     

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.     

Phase diagram of turbulence in superfluid 3He-B

No Heading In superfluid ³He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52–0.59 T_c and has a narrow width of 0.06 T_c while at zero pressure turbulence is not observed above 0.45 T_c.PACS numbers: 47.37, 67.40, 67.57     

Investigation of quantized circulation in superfluid 3He-B

We have studied circulation in superfluid ³He-B with a vibrating wire. We find that the circulation quantum equals h/2m ₃ to within experimental error at several pressures. We have also measured circulation in rotating superfluid ³He-B, and have observed a precessional motion of a single vortex line. Finally, we have found the unexpected result that circulation around the wire does not affect the pair-breaking critical velocity.     

Mobility of negative ions in superfluid 3He-B

We calculate the mobility of negative ions in superfluid ³He-B. We first derive the general formula for the mobility, and show that to a good approximation the scattering of quasiparticles from an ion may be treated as elastic, both in the superfluid for temperatures not too far below the transition temperature and also in the normal state. The scattering cross section in the superfluid is then calculated in terms of normal state properties; as we show, it is vital to include the effects of superfluid correlations on intermediate states in the scattering process. We find that for quasiparticles near the gap edge, the quasiparticle-ion scattering amplitude has a resonant behavior, and that as a result of interference among many partial waves, the differential scattering cross section is strongly peaked in the forward direction and reduced at larger angles, in much the same way as in diffraction. The transport cross section for such a quasiparticle is strongly reduced compared to that for a normal state quasiparticle, and the mobility is consequently strongly enhanced. Detailed calculations of the mobility which contain essentially no free parameters, agree well with the experimental data.This research was supported in part by U.S. National Science Foundation Grants DMR 75-22241, DMR 76-24011, DMR 78-21068, and DMR 78-21069.Niels Bohr Institute, University of Copenhagen     

The transverse acoustic response of superfluid3He-B

For both normal and superfluid³He, the propagation of a collisionless transverse sound mode is predicted. The study of this mode in the normal fluid has been problematic: it travels only slightly faster than the Fermi velocity and is very highly attenuated. Early theoretical results suggested that transverse sound would not propagate in the superfluid and the experimental study of this mode was not actively pursued. However, recent theoretical work has predicted that this mode should indeed propagate, at sufficiently high frequencies and low temperatures, due to the interaction with the imaginary squashing mode. We present here an extensive experimental study of the transverse acoustic response in the B phase of superfluid³He. These measurements were performed on a short path length (30.5 microns) acoustic cavity, using a continuous wave, single ended, acoustic impedance technique. Simultaneous measurements were made of the longitudinal acoustic response, on an adjacent acoustic cavity of similar geometry. Both sound modes were excited at a frequency of 61 MHz. With this arrangement, well understood features in the longitudinal acoustic response were used as fiducial points for the study of heretofore ambiguous or unobserved features in the transverse acoustic response. As predicted by recent theoretical calculations, the transverse acoustic response was markedly different when the sound frequency was greater than the imaginary squashing mode frequency, as compared to when the sound frequency was less than the imaginary squashing mode frequency. At lower pressures the transverse acoustic response clearly exhibited the signatures of an evolving standing wave pattern (with the transverse sound velocity much less than the longitudinal sound velocity), and as such provides convincing evidence of a propagating transverse mode.     

Collective-mode spectroscopy of textures in superfluid3He-B

A phenomenological theory for the propagation of the real squashing modes in superfluid³He-B is presented. This allows one to calculate the splitting of the real squashing (rsq) mode spectrum caused by the combined effects of magnetic field, dispersion, and texture in the experimentally important range of magnetic fields from 0 to 10³ Gauss. This serves to provide a tool for the rsq-mode spectroscopy of the -textures in³He-B. In particular, a new gyrosonic effect is suggested: the intensity of the rsq modes generated in textures depends on the sense of rotation—even when the axis of rotation coincides with the direction of the ultrasound propagation .     

Ballistic quasiparticle beam experiments in superfluid3He-B

In³He-B at temperatures of the order of 0.1T_c, where the meanfree path of the excitations measures several hundreds of metres, we are able to perform experiments on fully ballistic quasiparticle beams. We describe the first direct production and detection of a quasiparticle beam in superfluid ³ He with the use of a black-body radiator. The radiator may be used as a smoothly controllable continuous source and also as a bolometric detector, sensitive to a quasiparticle energy flux of order 100 fW mm ^–2 .     

Two phonon pair breaking in superfluid3He-B

We report on pulsed zero sound experiments in the B-phase of ³ He down to 0.6 mK. The investigated pressure and frequency range was 5 to 16 bar and 10 to 70 MHz, respectively. The dissipated energy during the sound pulses was between 0.4 to 90 nJ. The resolution in damping was about 0.1 cm ^–1 . Within the range of our experimental parameters we never observed two phonon absorption resulting from non-linear coupling of zero sound to the J =2⁺ mode. However, with pulses of single frequency a new peak structure was found at temperatures corresponding to (T) = . This behavior is attributed to pair breaking by two phonons of the same energy. The attenuation increased with increasing pulse power, but also depended on pulse duration. In addition to that, we found at all pressures and frequencies an unreproducible attenuation structure close to the position of the J=2⁺ mode.     

Theory of Josephson flow oscillations in superfluid3He-B

Avenel and Varoquaux have proposed an experiment for observing pressure-induced Josephson flow oscillations across an orifice connecting two reservoirs of³He-B. The aim of the present work is to specify the conditions for the observability of this effect. First the six coupled Ginzburg-Landau (GL) equations for the order parameter components within the orifice are solved, subject to rigid boundary conditions at the ends (fixed phase difference between the bulk order parameters) and specular reflection boundary conditions at the walls. The longitudinal component is depressed and one of the transverse components is enhanced toward the middle of the orifice. From the order parameter functions the supercurrent through the orifice I(), and the GL energyF() are calculated for 0 2 and for different lengths and cross sections of the orifice. A new feature of the functionI() in comparison to the current-phase relationship for superconducting microbridges is its multivaluedness and the occurrence of two nontrivial zeros ofI(). The functionF() exhibits two local maxima besides the absolute maximum at =. The optimal length of the orifice for the observability of the ac Josephson effect turns out to be about seven GL coherence lengths . Then the frequency of the Josephson flow oscillations, which follow the sudden application of a force F on a diaphragm, depends on F in a way similar to that in which the frequency of the parallel ringing experiment in³He-A depends on the field step H.     

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.     

Collective modes and spin waves in superfluid3He-B

Making use of a model Hamiltonian, which includes, besides the kinetic energy and the BCS-like pairing energy, the spin exchange energy as well as the dipolar interaction energy, we study theoretically the collective modes of the Balian - Werthamer state in the collisionless limit. In the absence of the dipolar interaction energy, the collective modes are classified according to their total angular momentumJ. Among 18 distinct modes, one mode withJ=0 and three modes withJ=1 are gapless. The latter modes couple with the spin fluctuation and are identified with spin wave modes. The effect of the dipolar interaction on these modes is discussed.Supported by the National Science Foundation.     

Spin dynamics of superfluid3He-B in a slab geometry

The spin dynamics and the spin relaxation mechanisms of the superfluid³He-B were studied by using the NMR method in a slab geometry, where the superfluid3He-B was confined between narrow parallel plates with a gap smaller than the healing length of then-texture and the magnetic field was applied parallel to the plates. The relaxation parameter in the Leggett-Takagi (LT) equations was determined from a line width measurement of the transverse CW NMR. By using the pulsed NMR method, spin dynamics were studied in the nonlinear region. The observed spin dynamics were in good agreement with a numerical calculation of the LT equations together with the relaxation parameter determined by the CW NMR. When the tipping angle became larger than a certain critical value, the superfluid³He-B entered the Brinkman-Smith (BS) state. In this case, we observed the slow relaxation process in the BS state and then the rapid recovery process from the BS state to the initial non-Leggett configuration. The slow process in the BS state was attributed to the surface relaxation mechanism due to the torque from the surface-field energy.     

Propagation of zero sound in superfluid3He-B under magnetic field

We present a theory of zero sound propagation in super fluid³He-B with an order parameter strongly distorted by magnetic field. A general formula of the dispersion relation for arbitrary magnetic field in the collisionless regime is derived within the weak coupling theory and under the assumption of particle-hole symmetry. The Landau parameters are taken into account up toF ₂ ^s andF ₀ ^a . Numerical results for the sound velocity and absorption spectrum are presented. We show that the collective modeJ = 1,J _z = 0 yields a sizable peak in the sound absorption spectrum under weak but finite magnetic field. The quasi-particle excitations under magnetic field also exhibit cusp-like fine structures in the absorption spectrum. We show that the anomalies discovered by Ling et al. and Sounders et al. near the pair breaking edge in theq H geometry consist of theJ = 1,J _z = 0 collective mode and the pair breaking cusps in theJ _z = 0, ±2 channels.     

Intrinsic and extrinsic mechanisms of vortex formation in superfluid3He-B

We report on the first comprehensive measurements of critical superflow velocities in³He-B which allow different mechanisms of vortex formation to be identified. As a function of temperatureT and pressureP, we measure the critical angular velocity Ω_c(T, P) at which vortices start to form in slowly accelerating rotation in a cylindrical container filled with³He-B. Owing to the long coherence length ξ(T, P)∼10–100 nm, either trapped remanent vorticity or intrinsic nucleation may dominate vortex formation, depending on the roughness of the container wall and the presence of loaded traps. NMR measurement with a resolution of one single vortex line allows us to distinguish between different processes: (1) Three extrinsic mechanisms of vortex formation have been observed. One of them is the vortex mill, a continuous periodic source which is activated in a rough-walled container well below the limit for intrinsic nucleation. (2) In a closed smooth-walled container intrinsic nucleation is the only mechanism available, with a critical velocity v_c(T, P)=Ω_c(T, P), whereR is the radius of the container. We findv _c (T, P) to be related to the calculated intrinsic stability limitv _ch (T, P) of homogeneous superflow. The existence of this connection in the form of a scaling law implies that nucleation takes place at an instability, rather than by thermal activation or quantum tunneling which become impossible because of an inaccessibly high energy barrier.     

Diffuse scattering model of the thermal damping of a wire moving through superfluid3He-B at very low temperatures

We present a microscopic model of the scattering of quasiparticles in superfluid³He-B by a moving solid surface. This is used to calculate the thermal damping of a wire resonator in the low temperature regime. The calculated damping force is in good agreement with experimental results when the quasiparticles are assumed to be scattered diffusely by the wire.     

Viscosity measurements in superfluid 3He-B from 2 to 29 bar

Measurements from a high-Q torsional oscillator and a vibrating wire are presented which give a consistent view of the viscosity of the normal fraction of ³He-B at high pressure. At low pressures discrepancies are largely eliminated by taking into account a mean-free-path size effect. We compare our corrected viscosities with recent calculations. The superfluid fraction, also measured in this experiment, is reexamined in the light of recent specific heat measurements.This work was conducted under NSF grant numbers DMR-78-02655 and DMR-77-24221 and through the Cornell Material Science Center, grant number DMR-78-15933.