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The Kelvin-Helmholtz instability is well known in classical hydrodynamics where it explains the sudden emergence of interfacial surface waves as a function of the flow velocity parallel to the interface. It can be carried over to the inviscid two-fluid dynamics of superfluids, to describe the stability of the phase boundary separating two bulk phases of superfluid $^{3}\mathrm{He}$ in rotating flow when the boundary is localized with a magnetic-field gradient. The results from extensive measurements as a function of temperature and pressure confirm that in the superfluid the classic condition for stability is changed and that the magnetic polarization of the $B$ phase at the phase boundary has to be taken into account, which yields the magnetic-field-dependent interfacial surface tension.

Andreev reflection of quasiparticle excitations from quantized line vortices is reviewed in the isotropic B phase of superfluid $^3$He in the temperature regime of ballistic quasiparticle transport at $T \leq 0.20\,T_\mathrm{c}$. The reflection from an array of rectilinear vortices in solid-body rotation is measured with a quasiparticle beam illuminating the array mainly in the orientation along the rotation axis. The result is in agreement with the calculated Andreev reflection. The Andreev signal is also used to analyze the spin down of the superfluid component after a sudden impulsive stop of rotation from an equilibrium vortex state. In a measuring setup where the rotating cylinder has a rough bottom surface, annihilation of the vortices proceeds via a leading rapid turbulent burst followed by a trailing slow laminar decay from which the mutual friction dissipation can be determined. In contrast to currently accepted theory, mutual friction is found to have a finite value in the zero temperature limit: $\alpha (T \rightarrow 0) = (5 \pm 0.5) \cdot 10^{-4}$., Comment: 14 pages, 10 figures, overview of Andreev reflection measurements in a rotating cylinder

In Fermi superfluids, like superfluid 3He, the viscous normal component can be considered to be stationary with respect to the container. The normal component interacts with the superfluid component via mutual friction which damps the motion of quantized vortex lines and eventually couples the superfluid component to the container. With decreasing temperature and mutual friction the internal dynamics of the superfluid component becomes more important compared to the damping and coupling effects from the normal component. This causes profound changes in superfluid dynamics: the temperature-dependent transition from laminar to turbulent vortex motion and the decoupling from the reference frame of the container at even lower temperatures., Comment: Extended version of the manuscript prepared for PNAS special feature on quantum turbulence

In superfluid 3He-B the damping of vortex motion varies many orders of magnitude in the currently accessible temperature range from T c to below 0.2 T c. The large variation in the dynamics switches on sequentially different processes of vortex formation as a function of temperature. These can be examined in a smooth-walled rotating cylinder in the absence of surface pinning. We provide an overview of vortex formation in spin-up and of annihilation in spin-down measurements at temperatures below the hydrodynamic transition at 0.6 T c where turbulence in the bulk volume becomes possible. Of central current interest are the very lowest temperatures at 0.2 T c where the dynamic processes reflect on the properties of the T→0 limit.

Rapidly evolving non-equilibrium phenomena, associated with phase transitions from meta-stable states, provide examples of most complex dynamics. Condensed matter many-particle quantum systems, which are described in terms of a coherent quantum field, are a particularly useful environment for such studies. Among them, the 3He superfluids display the largest variety of topological defects of different dimensionality and structure, owing to the large degree of freedom in the rearrangement of their multi-component p-wave order parameter field. A few measurements exist which monitor the non-equilibrium phase transition dynamics and display defect formation.

Oscillating objects such as discs, piles of discs, spheres, grids and wires have been widely used in cryogenic fluid dynamics and in quantum fluids research since the discovery of superfluidity. A new addition are quartz tuning forks, commercially available frequency standards. We review their use as thermometers, pressure- and viscometers as well as their potential as generators and detectors of cavitation and turbulence in viscous and superfluid He liquids.

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 \alpha(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 \Delta t 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 ~0.6T_c the number of remnants as a function of \alpha(T) and \Delta t. At temperatures below the transition to turbulence T \lesssim 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 \Delta t, applied flow velocity, and length of sample L., Comment: Submitted to the proceedings of the Quantum Fluids and Solids Conference 2006 (to be published in Journal of Low Temperature Physics 2007) New data are added

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

The Kelvin–Helmholtz instability takes place on the interface between two horizontally stratified fluid layers which are in a state of relative shear flow with respect to each other. The problem was solved for the ideal case of inviscid and incompressible fluids in 1871 by Lord Kelvin. The first case of superfluid shear flow has been discovered in uniformly rotating superfluid 3 He , when the phase boundary between the A and B phases is maintained at a stable location with a magnetic barrier field. At sufficiently high rotation the AB interface undergoes an instability, in which the interface becomes corrugated in a standing-wave pattern. The critical velocity of this process displays the temperature and magnetic field dependences which fit the characteristics of the Kelvin–Helmholtz instability.

The present generation of rotating refrigerators, which are used for the study of quantized vorticity in helium superfluids, are often capable of cooling to mK temperatures and rotate up to ∼ 1 rev/s. To achieve single-vortex resolution at all rotation velocities, smooth and stable rotation is required. This calls for low and stable rotational friction, sufficient axial alignment and lateral balancing of weights, to promote mechanical stability and precession-free rotation. We comment on general design principles, discuss the rotation noise spectrum of our installation, and describe interference problems from the rotation in low-noise measurement.

The double-quantum vortex line with continuous (singularity-free) structure is the most common linear defect in rotating 3 He-A. Its well-known experimental signature is a frequency-shifted satellite peak in the NMR spectrum. It arises from the absorption of spin wave excitations, which are localized bound states in the dipole-unlocked soft vortex core. In first approximation, the intensity of the satellite peak is proportional to the number of vortex lines. With increased measuring resolution we have found that the absorption contribution of individual vortex lines is not identical, but displays small variations, which depend on the non-uniform global orbital 1 texture. We attribute the effect to small texture-dependent changes in the 1 distribution in the soft core, which modify the attractive potential of the localized spin waves. This property can be used for studying the global order-parameter texture in the rotating container.

Sputtered Nb thin-film LC resonators for low frequencies at 0.5 MHz have been fabricated and tested in the temperature range 0.05--1 K in magnetic fields up to 30 mT. Their Q value increases towards decreasing temperature as sqrt(T) and reaches 10^3 at 0.05 K. As a function of magnetic field Q is unstable and displays variations up to 50%, which are reproducible from one field sweep to the next. These instabilities are attributed to dielectric losses in the plasma deposited SiO_2 insulation layer, since the thin-film coil alone reaches a Q > 10^5 at 0.05 K., 6 pages, 7 figures, submitted to Review of Scientific Instruments

Spin-mass vortices have been observed to form in rotating superfluid 3He−B, following the absorption of a thermal neutron and a rapid transition from the normal to the superfluid state. The spin-mass vortex is a composite defect which consists of a planar soliton (wall) which terminates on a linear core (string). This observation fits well within the framework of a cosmological scenario for defect formation, known as the Kibble-Zurek mechanism. It suggests that in the early Universe analogous cosmological defects might have formed.

We have investigated the NMR line shapes of superfluid 3He-B in a rotating cylinder. In the vortex-free state at sufficiently large angular velocity of rotation, Ω≳1 rad/s, the main feature of the absorption spectrum is a large frequency-shifted peak above the Larmor frequency. The shape of this counterflow peak is both measured and calculated as a function of external magnetic field strength, angular velocity, temperature, and number of vortex lines. The NMR spectrum is derived from the calculated order-parameter texture. Reasonable agreement with the measured line shape is obtained by including line-broadening effects due to the external field inhomogeneity and Leggett–Takagi relaxation.

Nonlinear spin precession has been observed in 3He-B in large counterflow of the normal and superfluid fractions. The new precessing state is stabilized at high rf excitation level and displays frequency-locked precession over a large range of frequency shifts, with the magnetization at its equilibrium value. Comparison to analytical and numerical calculation indicates that in this state the orbital angular momentum L of the Cooper pairs is oriented transverse to the external magnetic field in a ``non-Leggett'' configuration with broken spin-orbit coupling. The resonance shift depends on the tipping angle theta of the magnetization as omega - omega_L = (Omega_B^2 / 2 omega_L)(cos(theta) - 1/5). The phase diagram of the precessing modes with arbitrary orientation of L is constructed., Comment: Revtex file, 5 pages, 4 figures, version submitted to Phys. Rev. Lett

The maximum and the equilibrium numbers of vortex lines are measured in a rotating cylindrical container as a function of its rotation velocity Ω. We find that a slow cool-down through the superfluid transition at constant rotation produces a state with the equilibrium number of lines, Neq(Ω). In decelerating rotation, when vortex lines annihilate, the state is obtained which includes the maximum possible number of lines, Nmax(Ω). At low velocities Nmax(Ω) exceeds Neq(Ω) and the surplus Nmax−Neq is stabilized by an annihilation energy barrier, which during further deceleration ultimately vanishes in an instability. At high velocities extrinsic effects, such as a misalignment between the container and rotation axes, remove the annihilation barrier and cause Nmax to equal Neq. Our analysis concludes that the lowest annihilation barrier is provided by the bending of the peripheral vortex lines at one end of the container and not by collective instability in the peripheral shape of the vortex array.

We use neutron absorption in rotating 3He-B to heat locally a 10 micrometer-size volume into normal phase. When the heated region cools back in microseconds, vortex lines are formed. We record with NMR the number of lines as a function of superflow velocity and compare to the Kibble-Zurek theory of vortex-loop freeze-out from a random network of defects. The measurements confirm the calculated loop-size distribution and show that also the superfluid state itself forms as a patchwork of competing A and B phase blobs. This explains the A to B transition in supercooled neutron-irradiated 3He-A., RevTex file, 4 pages, 3 figures, resubmitted to Phys. Rev. Lett

A superconducting 100 μm planar coil has been tested for low field cw NMR. The nine-turn 5 nH coil is connected via a planar 1:8 step-up transformer to an external parallel capacitor and resonated at 0.8 MHz to give a Q of 350. The tank circuit voltage is measured with a liquid He temperature GaAs MESFET preamplifier. Test experiments have been conducted by immersing the Si chip with the planar pick-up coil in liquid and solid3He to measure their cw NMR absorptions in the temperature range 0.05 – 0.5 K.

The cw NMR response of 3 He-B is investigated in large rf excitation fields, which exceed in magnitude the equivalent of the spin-orbit coupling. New states of stable spin precession are observed. The Leggett-Takagi spin-dynamic equations are solved numerically with the proper experimental parameters, the results are found to reproduce most of the experimental features, and allow an identification of the new modes. Vortex lines or vortex-free counterflow in the rotating superfluid have not been found to influence the measured NMR signatures of the new modes.

In decelerating rotation, vortex lines annihilate in single-vortex events at the annihilation threshold where their number ${N}_{\mathrm{}\mathrm{max}}(\ensuremath{\Omega})$ is equal to or exceeds the equilibrium value ${N}_{\mathrm{}\mathrm{eq}}(\ensuremath{\Omega})$. A surplus ${N}_{\mathrm{max}}\ensuremath{-}{N}_{\mathrm{eq}}$ may be stabilized by an energy barrier, which during deceleration vanishes in an instability. We find the barrier to depend on container misalignment in ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}B$ and on the orbital texture in the container corners in ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A$. Measurements of the instability yield the circulation quantum of the vortex which is found to be consistent with the present identification of vortex structures in ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A$.

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 Ωc(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 vc(T, P)=Ωc(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.

In superfluid $^3$He-B externally pumped quantized spin-wave excitations or magnons spontaneously form a Bose-Einstein condensate in a 3-dimensional trap created with the order-parameter texture and a shallow minimum in the polarizing field. The condensation is manifested by coherent precession of the magnetization with a common frequency in a large volume. The trap shape is controlled by the profile of the applied magnetic field and by the condensate itself via the spin-orbit interaction. The trapping potential can be experimentally determined with the spectroscopy of the magnon levels in the trap. We have measured the decay of the ground state condensates after switching off the pumping in the temperature range $(0.14\div 0.2)T_{\mathrm{c}}$. Two contributions to the relaxation are identified: (1) spin-diffusion with the diffusion coefficient proportional to the density of thermal quasiparticles and (2) the approximately temperature-independent radiation damping caused by the losses in the NMR pick-up circuit. The measured dependence of the relaxation on the shape of the trapping potential is in a good agreement with our calculations based on the magnetic field profile and the magnon-modified texture. Our values for the spin diffusion coefficient at low temperatures agree with the theoretical prediction and earlier measurements at temperatures above $0.5T_{\mathrm{c}}$., Comment: 15 pages, 6 figures, manuscript prepared for International Symposium on Quantum Fluids and Solids 2013. The final publication is available at http://link.springer.com/article/10.1007/s10909-013-0946-y

NMR spectrometry can be used to identify different topological objects in the order parameter field of rotating superfluid3He-A. We list their signatures in the cw NMR absorption line shape. Quantized vortex lines, domain walls, and their combination, the vortex sheet, all induce satellite peaks with specific intensities and frequency shifts in the NMR spectrum. Examples of spectra are presented to allow a comparison and to distinguish between different objects.

A superfluid in the absence of a viscous normal component should be the best realization of an ideal inviscid Euler fluid. As expressed by d’Alembert’s famous paradox, an ideal fluid does not drag on bodies past which it flows, or in other words it does not exchange momentum with them. In addition, the flow of an ideal fluid does not dissipate kinetic energy. Here we study experimentally whether these properties apply to the flow of superfluid 3He-B in a rotating cylinder at low temperatures. It is found that ideal behaviour is broken by quantum turbulence, which leads to substantial energy dissipation, as was also observed earlier. Remarkably, the angular momentum exchange between the superfluid and its container approaches nearly ideal behaviour, as the drag almost disappears in the zero-temperature limit. Here the mismatch between energy and angular momentum transfer results in a new physical situation, with severe implications on the flow dynamics.

Coherent quantum states of different chirality have been formed and identified in the A phase of superfluid helium-3, confirming previous theoretical predictions.

Four alternative but topologically different structures of vorticity exist in rotating ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A$. As a function of magnetic field ( $H$) and rotation velocity $(\ensuremath{\Omega})$, we identify with NMR the type of vortex which is nucleated during cooling from the normal to the superfluid phase. The measurements are compared to the calculated equilibrium phase diagram of vortices in the $H\ensuremath{-}\ensuremath{\Omega}$ plane at temperatures $T\ensuremath{\lesssim}{T}_{c}$. Slow transitions are found to reproduce the calculated equilibrium state.

Nucleation of vortices in units of one quantum has been observed with c.w. NMR in a rotating cylinder filled with 3He-B. During acceleration a new vortex is created each time the counterflow velocity at the perimeter reaches a critical value vc(T, p). The measured vc resembles the calculated velocity vcb(T, p) of the bulk superflow instability, but is smaller by a factor with power law dependence on the superfluid coherence length. This indicates that a nucleation event takes place whenever the flow exceeds vcb locally at the nucleation site and the nucleation barrier vanishes.

How do vortex lines in the A and B phases of superfluid 3 He interact at the AB phase boundary, when they have different structure and quantization in these two phases? We discuss an experimental setup where the AB interface is stabilized in a long cylindrical sample with a magnetic barrier field. It divides the sample in A- and B-phase sections which are maintained in homogeneous low-field NMR environments over the temperature interval where the supercooled A phase exists. With two independent NMR spectrometers the vortex lines in the two phases can be studied as a function of the rotation velocity of the cryostat. Simultaneously, by adjusting the barrier field and temperature, the sample can be changed from single phase to two-phase configurations, or to one with two AB interfaces. Using this setup the first example of a shear-flow instability in superfluids was discovered (Phys. Rev. Lett. 89 (2002) 155 301).

We report on direct measurements of the energy dissipated in the spin-up of the superfluid component of 3He-B. A vortex-free sample is prepared in a cylindrical container, where the normal component rotates at constant angular velocity. At a temperature of 0.20Tc, seed vortices are injected into the system using the shear-flow instability at the interface between 3He-B and 3He-A. These vortices interact and create a turbulent burst, which sets a propagating vortex front into motion. In the following process, the free energy stored in the initial vortex-free state is dissipated leading to the emission of thermal excitations, which we observe with a bolometric measurement. We find that the turbulent front contains less than the equilibrium number of vortices and that the superfluid behind the front is partially decoupled from the reference frame of the container. The final equilibrium state is approached in the form of a slow laminar spin-up as demonstrated by the slowly decaying tail of the thermal signal., Comment: 12 pages, 5 figures, to appear in Journal of Low Temperature Physics

A new state of rotating superfluid $^{3}\mathit{A}$ has been found. Instead of quantized vortex lines, it consists of a continuous vortex sheet. The sheet has as a backbone a topologically stable domain wall called soliton, to which the vorticity is bound. The sheet folds to equidistant layers that fill uniformly the rotating container. The new state can easily be created experimentally in spite of its higher energy. Its identification is deduced from nuclear magnetic resonance.

Quantized vortices, when formed in rotating 3 He, can effectively be studied by NMR. Vortices of different structure have been identified, depending on the superfluid phase and the external conditions. Here we discuss what happens when the first-order phase boundary, which separates the A and B phases, traverses through a rotating container which initially contains an equilibrium vortex array. The measurements imply that a vortex layer is formed in front of a slowly propagating interface and part of the newly formed phase behind the interface is left devoid of vortices.

In a rotating two-phase sample of ${}^{3}$He-$B$ and magnetic-field stabilized ${}^{3}$He-$A$ the large difference in mutual friction dissipation at $0.20{T}_{\mathrm{c}}$ gives rise to unusual vortex flow responses. We use noninvasive NMR techniques to monitor spin down and spin up of the $B$-phase superfluid component to a sudden change in the rotation velocity. Compared to measurements at low field with no $A$ phase, where these responses are laminar in cylindrically symmetric flow, spin down with vortices extending across the $AB$ interface is found to be faster, indicating enhanced dissipation from turbulence. Spin up in turn is slower, owing to rapid annihilation of remanent vortices before the rotation increase. As confirmed by both our NMR signal analysis and vortex filament calculations, these observations are explained by the additional force acting on the $B$ phase vortex ends at the $AB$ interface.

Long-lived coherent spin precession of $^{3}\mathrm{He}\mathrm{\text{\ensuremath{-}}}\mathrm{B}$ at low temperatures around $0.2{T}_{c}$ is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.

Steady-state turbulent motion is created in superfluid 3He-B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of 3He-B and replaces vortex-free flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2 Tc during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e. the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit., Comment: 4 pages, 4 figures

Measurements of the order parameter texture of rotating superfluid 3He-B have been performed as a function of the applied azimuthal counterflow velocity down to temperatures of 0.2 T c. The results are compared to the hydrostatic theory of 3He-B. Good agreement is found at all measured temperatures and rotation velocities when the flow anisotropy contribution to the textural free energy is adjusted. This gives a superfluid energy gap Δ(T) which agrees with that measured by Todoshchenko et al., with Δ(0)=1.97 k B T c at 29.0 bar. The B-phase susceptibility, longitudinal resonance frequency, and textural phase transition have been extracted from the measurements as a function of temperature and azimuthal counterflow velocity. Owing to decreasing absorption intensities the present measuring method, based on the line shape analysis of the NMR spectrum, loses its sensitivity with decreasing temperature. However, we find that in practice the measurement of vortex numbers and counterflow velocities is still feasible down to 0.2 T c.

We describe the first measurement on Andreev scattering of thermal excitations from a vortex configuration with known density, spatial extent, and orientations in 3He-B superfluid. The heat flow from a blackbody radiator in equilibrium rotation at constant angular velocity is measured with two quartz tuning fork oscillators. One oscillator creates a controllable density of excitations at 0.2Tc base temperature and the other records the thermal response. The results are compared to numerical calculations of ballistic propagation of thermal quasiparticles through a cluster of rectilinear vortices., Comment: 6 pages, 4 figures

Using NMR techniques we monitor the structure and number of vortices in a cylindrical container, rotating at constant angular velocity Ω, before and after the passage of the A-B interface. The initial A phase contains the equilibrium number of vortices. The final B phase is found to have a deficit of vortices which depends nonmonotonically on the measured time t AB of the A→B transition. We argue that a vortex layer is formed in front of the moving A-B interface. The measured vortex deficit can be understood by analyzing the stability of the layer

Insight in the dynamics of quantized vortex lines has been obtained by performing NMR measurements in uniformly rotating superfluid [sup 3]He-[ital B]. Compared to superfluid [sup 4]He, in [sup 3]He-[ital B] the viscosity of the normal component is three orders of magnitude larger and the pinning of vortices is weaker. The collective modes governing the hydrodynamic response of an array of vortex lines are highly overdamped. Two distinct modes are identified: (1) a relatively fast mutual-friction-resisted mode, which controls the redistribution of the vortex density on a time scale of a few seconds, and (2) an exponentially relaxing slow mode with a time constant of a few minutes, which governs asymptotically the approach to equilibrium at nearly constant vortex density. Measurement of the fast motion allows us to extract the dissipative mutual friction. The slow mode is dominated by the elastic tension along the vortex line and by weak pinning at the top and bottom surfaces of the rotating container. With increasing vortex density the surface pinning becomes a collective process, in which coherently moving groups of vortices are pinned in unison. Collective pinning is a result of the shear elasticity related to the crystalline order of the vortex lattice.more » Our measurements on the slow mode indicate that the crystalline correlation extends over many lattice spacings.« less

In the superfluid phases of [sup 3]He quantized vortex lines have been investigated under uniform rotation, when they form a regular array of rectilinear objects. A large diversity exists in the structure and properties of vortices, owing to the complicated nature of symmetry breaking in the different superfluid phases. A review is presented here on the various experimentally verified types of vortices. Recent measurements open a puzzling problem about their interaction and interconnection at the first-order phase boundary separating the A and B phases of superfluid [sup 3]He.

Exponentially damped relaxation with a time constant (1 ÷ 3) min after perturbation of steady rotation has been discovered in rotating 3He-B, using NMR techniques. The effect represents an overdamped collective mode of the vortex array, governed by vortex tension and pinning. Elastic-shear deformation of the array is found to influence pinning, but does not contribute in the bulk liquid. The presence of shear elasticity provides the first evidence for crystalline order of a vortex array in 3He.

We have observed spin-mass vortices (SMV) in rotating superfluid $^{3}\mathit{B}$. The SMV is a combined topological object formed of an ordinary vortex with mass current and of a disclination with spin current. A planar defect, so-called \ensuremath{\theta} soliton, is topologically bound to the SMV line. The SMV's were created primarily by cooling the $^{3}\mathrm{He}$ sample through a reversible A\ensuremath{\rightarrow}B transition at a constant rotation velocity, which was smaller than the critical velocity for the nucleation of vortices ${\mathrm{in}}^{3}$He-B. The observation of the SMV's is based on changes in the NMR absorption caused by the attached solitons: The absorption is shifted to higher frequencies in conventional NMR at low rf excitation and large additional absorption is observed in the homogeneously precessing domain (HPD) at high excitation. The presence of SMV's is deduced from the stability and from the rotation-speed dependence of the additional absorption.

A central question in the dynamics of vortex lines in superfluids is dissipation on approaching the zero temperature limit T → 0. From both NMR measurements and vortex filament calculations, we find that vortex flow remains laminar up to large Reynolds numbers Re α ∼ 10 3 in a cylinder filled with 3 He-B. This is different from viscous fluids and superfluid 4 He, where the corresponding responses are turbulent. In 3 He-B, laminar vortex flow is possible in the bulk volume even in the presence of sizable perturbations from axial symmetry to below 0.2T c . The laminar flow displays no excess dissipation beyond mutual friction, which vanishes in the T → 0 limit, in contrast with turbulent vortex motion where dissipation has been earlier measured to approach a large T-independent value at T ≲ 0.2T c .

In transverse NMR at high rf excitation, it is possible to separate a [sup 3]He-[ital B] sample into two magnetic domains. In one domain the spins are precessing coherently with a large tilting angle in relation to the polarizing magnetic field while in the other they are stationary and oriented parallel to the field. We have studied the two-domain system during vortex-free rotation and found that the boundary region between the precessing and static domains is sensitive to superfluid counterflow, flowing parallel to the boundary. The volume of the precessing domain decreases and the NMR absorption, associated with spin diffusion across the boundary, increases. The shift of the domain boundary is analyzed in terms of the competition between the kinetic energy of counterflow and the gradient in the Zeeman energy. From the shift we obtain the superfluid density anisotropy, induced by the magnetic field. A calculation in the weak-coupling approximation explains only half of the measured ansiotropy at low pressures. At high pressures the discrepancy is smaller.

We have observed spin-mass vortices (SMV) in superfluid $^{3}\mathit{B}$. The SMV is a combined topological object made up of a vortex line with mass current and a disclination line with spin current. It is also a termination line of a planar defect, the so-called \ensuremath{\theta} soliton. The SMVs are bound either as pairs or to the container wall by the soliton. They are nucleated when a rotating $^{3}\mathrm{He}$ sample cools slowly through the A\ensuremath{\rightarrow}B phase transition. The identification of the SMV is based on the NMR signatures of the soliton.

In rotating 3He-B the critical flow velocity for the nucleation of singular vortex lines is high and allows the existence of different rotating states: vortex-free counterflow, the equilibrium vortex state, and metastable states with a well-defined vortex cluster containing less than the equilibrium number of vortices. These states can be distinguished and characterized using CW NMR techniques. We derive an estimate for the magnetic field induced anistropy of the superfluid energy gap from an analysis of the spatial distribution of the order parameter texture in the vortex-free state. When vortices are introduced, their number in the vortex cluster can be counted using a simple experimental procedure. This allows us to measure the critical rotation velocity for the nucleation of vortices, which proves to correspond to the maximum flow velocity in the cylindrical NMR cell.

New techniques, both for generating and detecting turbulence in the helium superfluids 3 He-B and 4 He, have recently given insight in how turbulence is started, what the dissipation mechanisms are, and how turbulence decays when it appears as a transient state or when externally applied turbulent pumping is switched off. Important simplifications are obtained by using 3 He-B as working fluid, where the highly viscous normal component is practically always in a state of laminar flow, or by cooling 4 He to low temperatures where the normal fraction becomes vanishingly small. We describe recent studies from the low temperature regime, where mutual friction becomes small or practically vanishes. This allows us to elucidate the mechanisms at work in quantum turbulence on approaching the zero temperature limit.

We present experimental proof that in rotating {sup 3}He-{ital B} the vortex-core transition temperature {ital T}{sub {ital V}} separates axisymmetric vortices above {ital T}{sub {ital V}} from vortices with spontaneously broken axial symmetry below {ital T}{sub {ital V}}. The nonaxisymmetry is observed in the presence of coherent spin precession as a new soft Goldstone mode, manifested as oscillations and spiral twisting of the core anisotropy axis. These are driven by the precessing spin via spin-orbit coupling and lead to magnetic relaxation from viscous losses, which depend on vortex pinning.