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.     

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.      

Thermal Detection of Turbulent and Laminar Dissipation in Vortex Front Motion

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 0.20T _c, 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.     

Phase transitions in the growth of4He films

Using a microscopic, variational approach we examine the growth of⁴He absorbed to graphite and alkali substrates. We find that superfluid layers are formed and their behavior as a function of coverage is closely related to the one of a purely two-dimensional superfluid. The growth of a new layer undergoes a phase transition from a cluster formation into the connected superfluid when the coverage is increased. Based on the important connection to the two-dimensional fluid we propose a microscopic theory of quantum vortices in⁴He films at zero temperature, in which single vortices are treated as quasiparticles. We calculate the energy needed to create the single vortex, vortex inertial mass, microscopic interaction between vortices and binding energy of the vortex-antivortex pair as a function of density. We predict that at the⁴He superfluid density less than about 0.037 Å^–2 the binding energy of the pair becomes negative, indicating a phase transition into a new state where vortex-antivortex pairs are spontaneously created.     

Vortex Formation in Neutron-Irradiated Rotating Superfluid 3He-B

A convenient method to create vortices in meta-stable vortex-free superflow of ³He-B is to irradiate with thermal neutrons. The vortices are then formed in a rapid non-equilibrium process with distinctive characteristics. Two competing explanations have been worked out about this process. One is the Kibble-Zurek mechanism of defect formation in a quench-cooled second order phase transition. The second builds on the instability of the moving front between superfluid and normal ³He, which is created by the heating from the neutron absorption event. The most detailed measurements with single-vortex resolution have been performed at temperatures close to T_c. In the first half of this report we summarize the two models and then show that the experimentally observed vortices originate from the Kibble-Zurek mechanism. In the second half we present new results from low temperatures. They also weakly support the Kibble-Zurek origin, but in addition display superfluid turbulence as a new phenomenon. Below 0.6 T_c the damping of vortex motion from the normal component is reduced sufficiently so that turbulent vortex dynamics become possible. Here a single absorbed neutron may transfer the sample from the meta-stable vertex-free to the equilibrium vortex state. The probability of a neutron to initiate a turbulent transition grows with increasing superflow velocity and decreasing temperature. PACS numbers: 47.32, 67.40, 67.57, 98.80.     

Transition to Superfluid Turbulence

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid ³He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction—the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of the dynamics is vortex number conserving, while at low friction and large vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of ³He-A and ³He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin–Helmholtz instability.      

Propagation of Quantized Vortices Driven by an Oscillating Sphere in Superfluid 4He

We performed numerical simulation of quantum turbulence at 0 K generated from remnant vortices attached to an oscillating sphere. The remnant vortices are extended by the sphere motion and form a tangle with emitting vortex loops. As time passes, the length of vortices in a computational volume becomes statistically steady. We investigate in the statistical steady state the distribution of the length of vortex loops and anisotropy of their propagation direction caused by the sphere oscillation. The propagation direction of the emitted vortex loops is anisotropic along the oscillation direction of the sphere. The obtained results are consistent with results obtained in the experimental study using vibrating wires in superfluid ⁴He.     

Dynamics of Quantized Vortices in a Rotating Cylindrical Vessel

Recently Finne et al. found a transition to the turbulent state in rotating superfluid ³He-B which is insensitive to the fluid velocity, but rather controlled by temperature. They reported that at low temperatures a few seed vortices, injected into a vortex-free region, developed through a transient turbulent state to a vortex array. The experimental observations were consistent with the numerical simulation of dynamics of quantized vortices. However, we do not understand well how the seed vortex follows the above scenario and, especially, how the turbulent vortices change to a vortex array. Although the previous numerical simulation was done for a rotating cubic vessel, we study here the vortex dynamics in a rotating cylindrical vessel which is more suitable for the comparison with the experiments. We developed a numerical method for calculating the vortex dynamics in a cylindrical vessel and investigated the vortex dynamics after a vortex seed loop was injected into a vortex-free region. The numerical result shows that the seed vortex becomes unstable, especially near the cylindrical side wall, and develops into turbulent vortices. After that a vortex array appears in the central region, collecting the vortices from the surrounding tangle. PACS numbers: 67.40.Vs, 47.32.Cc, 47.37.+q.     

Observations of Vortex Emissions from Superfluid 4He Turbulence at High Temperatures

An immersed object with high velocity oscillations causes quantum turbulence in superfluid ⁴He, even at very low temperatures. The continuously generated turbulence may emit vortex rings from a turbulent region. In the present work, we report vortex emissions from quantum turbulence in superfluid ⁴He at high temperatures, by using three vibrating wires as a turbulence generator and vortex detectors. Two detector wires were mounted beside a generator wire: one in parallel and the other in perpendicular to the oscillation direction of the generator. The detection times of vortex rings represent an exponential distribution with a delay time t ₀ and a mean detection period t ₁. The delay time includes the generation time of a fully developed turbulence and the time-of-flight of a vortex ring. At high temperatures, vortices are dissipated by relative motion between a normal fluid component and the vortices, resulting that only large vortex rings are reachable to the detectors. Using this method, we detected vortex rings with a diameter of 100 μm, comparable to a peak-to-peak vibration amplitude of 104 μm of the generator. The large vortices observed here are emitted anisotropically from the generator. The emissions parallel to the vibrating direction are much less than those perpendicular to the direction.     

Experiments on the Twisted Vortex State in Superfluid 3He-B

We have performed measurements and numerical simulations on a bundle of vortex lines which is expanding along a rotating column of initially vortex-free ³He-B. Expanding vortices form a propagating front: Within the front the superfluid is involved in rotation and behind the front the twisted vortex state forms, which eventually relaxes to the equilibrium vortex state. We have measured the magnitude of the twist and its relaxation rate as function of temperature above 0.3T _c. We also demonstrate that the integrity of the propagating vortex front results from axial superfluid flow, induced by the twist.      

Dissipation and Phase Slip in Confined Superfluid Helium: Evidence for an Equilibrium Distribution of Vortices

The effects of phase slip due to the thermal creation of vortices in confined liquid ⁴He below the point is discussed. In a narrow tube there is a finite probability of thermal activation of a vortex in the superfluid helium, with the vortex not parallel to the axis of the tube. In the presence of a heat flow along the tube, the vortices experience the Magnus force, which prevents exact cancellation of the motion of thermally activated vortices traversing the cross section of the tube in opposite directions. Each crossing of the tube by a vortex causes a 2 phase slip of the superfluid order parameter along the tube. A temperature gradient results, which is proportional to the rate of phase slip, thus yielding a nonvanishing thermal resistivity below the bulk point. The calculated temperature dependence compares well with experimental data, thereby providing indirect evidence of the presence of vortices in thermal equilibrium.     

The generation of particles to observe quantized vortex dynamics in superfluid helium

We describe a method to prepare a sample of superfluid helium-4 with hydrogen particles suspended within it. The method is to dilute hydrogen gas with helium at room temperature, and bubble the mixture through liquid helium at a temperature above the superfluid phase transition temperature, T_λ ≈ 2.17 K. The procedure yields a suspension of micron-sized particles whose total volume is about 10⁵ times smaller than the fluid volume. The fluid and suspension are then cooled to a temperature below T_λ. We show that the particles, so prepared in superfluid helium, are useful for studying superfluid flows and, in particular, the dynamics of quantized vortices. In addition, the particle-superfluid helium system is rich in not yet fully explained interactions. We review preliminary investigations that include observing the vortex lattice in rotating helium, vortex reconnection in quantized vortex turbulence, and vortex ring decay. These data illustrate the basic mechanisms of dissipation in superfluid turbulence.     

Vortex Rings in Superfluid 3He–B at Low Temperatures

Turbulence in classical fluids has far-reaching technological implications but is poorly understood. A better understanding might be gained from studying turbulence in quantum systems. In a pure superfluid (at low temperatures), there is no viscosity and vortex lines are quantised. Quantum turbulence consists of a tangle of quantised vortex lines which interact via their self-induced flow. We have recently developed techniques for detecting vortices in superfluid ³He–B in the low temperature limit. We find that the transition to turbulence from a moving grid occurs by the entanglement of emitted vortex rings. Here, we discuss the propagation of the ballistic vortex rings emitted at low grid velocities. We have measured the temperature at which the rings decay before reaching the detectors. Our results, at two different pressures, confirm that the vortex rings decay in accordance with mutual friction.     

Time-of-Flight Experiments of Vortex Rings Propagating from Turbulent Region of Superfluid 4He at High Temperature

We report the time-of-flight of quantized vortex rings generated by a vibrating wire in superfluid ⁴He which contains normal fluid component. A cover box of vibrating wires and slow cooling of superfluid reduce the number of vortices attached to wire surfaces, enabling us to study vortex rings propagating from a turbulent region. Using two vibrating wires as a generator and a detector of vortices, the time-of-flight of vortices propagating a distance of 0.88 mm was measured at 1.25 K. We find that the time-of-flights distribute from 0.06 s to 27.4 s, much larger than the lifetimes of circular vortex rings limited in the size of a generator amplitude. These results imply that large vortex rings with non-circular shape or vortex tangles are created by the generator, propagating slowly and colliding with the detector before complete disappearance.     

Experiments on the Vortex Dynamics in Superfluid 4He with no Normal Component

We report results from ongoing experiments on the dynamics of quantized vortices in superfluid ⁴He at temperatures below 0.2 K. Charged vortex rings of micron size were used to detect the presence of vortices, to create a turbulent tangle, and to charge an array of rectilinear vortex lines. The results reveal that the ion technique has great potential for the study of vortices in ⁴He at very low temperatures.     

Vortices and Dynamics in Trapped Bose-Einstein Condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schrödinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid ⁴He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.     

Superfluid 3He-B Vortex Simulations inside a Rotating Cylinder

No Heading We study numerically vortex dynamics in superfluid ³He-B by solving the full Biot-Savart equations inside a rotating cylinder. The initial vortex configuration seems to have an essential role whether the growth process starts or not. The growth process is, at least at the early stages of simulations, mostly governed by the reconnections with cylinder boundary. In order to see a large increase in vortex density one should go below 0.5T_c in temperature, somewhat lower than what is observed in the experiments.PACS numbers: 47.32, 67.57.     

Dissipation and Phase Slip in Confined Superfluid 4He

We give a brief summary of some results that are to appear elswhere. We have studied a vortex-related mechanism for the non-vanishing thermal resistance well below the bulk lambda point of liquid ⁴He confined in a long cylinder. Here we outline the main concept of the proposed physical mechanism. It involves the non-equilibrium distribution of vortices in the steady state when a small heat current flows along the cylinder axis. We have found that the probability of the saddle-point vortex configuration, which depends exponentially on the length of the vortex, scaled in units of the superfluid correlation length, is the dominant factor in the thermal resistance.     

Particles-Vortex Interactions and Flow Visualization in 4He

Recent experiments have demonstrated a remarkable progress in implementing and use of the Particle Image Velocimetry (PIV) and particle tracking techniques for the study of turbulence in ⁴He. However, an interpretation of the experimental data in the superfluid phase requires understanding how the motion of tracer particles is affected by the two components, the viscous normal fluid and the inviscid superfluid. Of a particular importance is the problem of particle interactions with quantized vortex lines which may not only strongly affect the particle motion, but, under certain conditions, may even trap particles on quantized vortex cores. The article reviews recent theoretical, numerical, and experimental results in this rapidly developing area of research, putting critically together recent results, and solving apparent inconsistencies. Also discussed is a closely related technique of detection of quantized vortices by negative ion bubbles in ⁴He.     

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