Quantized Vortex Rings Research Articles

Kelvin waves from vortex reconnection in superfluid helium at low temperatures

We report on the analysis of the root mean square curvature as a function of the numerical resolution for a single reconnection of two quantized vortex rings in superfluid helium. We find a similar scaling relation as reported in the case of decaying thermal counterflow simulations by L. Kondaurova et al. There the scaling was related to the existence of a Kelvin-wave cascade which was suggested to support the L'vov-Nazarenko spectrum. Here we provide an alternative explanation that does not involve the Kelvin-wave cascade but is due to the sharp cusp generated by a reconnection event in a situation where the maximum curvature is limited by the computational resolution. We also suggest a method for identifying the Kelvin spectrum based on the decay of the rms curvature by mutual friction. Our vortex filament simulation calculations show that the spectrum of Kelvin waves after the reconnection is not simply $n(k) \propto k^{-\eta}$ with constant $\eta$. At large scales the spectrum seems to be close to the Vinen prediction with $\eta$ = 3 but becomes steeper at smaller scales.

A Note on the Propagation of Quantized Vortex Rings Through a Quantum Turbulence Tangle: Energy Transport or Energy Dissipation?

We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high resolution numerical simulations we examine the validity of simple estimates of the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately $75\%$ of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipation.

Reconnections of quantized vortex rings in superfluid 4He at very low temperatures.

Collisions in a beam of unidirectional quantized vortex rings of nearly identical radii R in superfluid 4He in the limit of zero temperature (0.05 K) were studied using time-of-flight spectroscopy. Reconnections between two primary rings result in secondary vortex loops of both smaller and larger radii. Discrete steps in the distribution of flight times, due to the limits on the earliest possible arrival times of secondary loops created after either one or two consecutive reconnections, are observed. The density of primary rings was found to be capped at the value 500 cm-2R-1 independent of the injected density. This is due to collisions between rings causing the piling up of many other vortex rings. Both observations are in quantitative agreement with our theory.

Communication: Nucleation of quantized vortex rings in 4He nanodroplets

Whereas most of the phenomena associated with superfluidity have been observed in finite-size helium systems, the nucleation of quantized vortices has proven elusive. Here we show using time-dependent density functional simulations that the solvation of a Ba(+) ion created by photoionization of neutral Ba at the surface of a (4)He nanodroplet leads to the nucleation of a quantized ring vortex. The vortex is nucleated on a 10 ps timescale at the equator of a solid-like solvation structure that forms around the Ba(+) ion. The process is expected to be quite general and very efficient under standard experimental conditions.

Quantized Superfluid Vortex Rings in the Unitary Fermi Gas

In a recent article, Yefsah et al. [Nature (London) 499, 426 (2013)] report the observation of an unusual excitation in an elongated harmonically trapped unitary Fermi gas. After phase imprinting a domain wall, they observe oscillations almost an order of magnitude slower than predicted by any theory of domain walls which they interpret as a "heavy soliton" of inertial mass some 200 times larger than the free fermion mass or 50 times larger than expected for a domain wall. We present compelling evidence that this "soliton" is instead a quantized vortex ring, by showing that the main aspects of the experiment can be naturally explained within the framework of time-dependent superfluid density functional theories.

Optical tweezers for vortex rings in Bose-Einstein condensates

We study generation and stabilization of vortex rings in atomic Bose-Einstein condensates. We suggest an approach for generating vortex rings by optical tweezers---two blue-detuned optical beams forming a toroidal void in a magnetically or optically confined condensate cloud. We demonstrate that matter-wave vortex rings trapped within the void are energetically and dynamically stable. Our theoretical findings suggest a possibility for the generation, stabilization, and nondestructive manipulation of quantized vortex rings in experimentally feasible trapping configurations.

Cross-sections of Andreev scattering by quantized vortex rings in3He-B

We studied numerically the Andreev scattering cross-sections of three-dimensional isolated quantized vortex rings in superfluid 3 He-B at ultralow temperatures. We calculated the dependence of the cross-section on the ring's size and on the angle between the beam of incident thermal quasiparticle excitations and the direction of the ring's motion. We also introduced, and investigated numerically, the cross-section averaged over all possible orientations of the vortex ring; such a cross-section may be particularly relevant for the analysis of experimental data. We also analyzed the r

Smoke Ring Physics

The behavior of smoke rings, tornados, and quantized vortex rings in superfluid helium has many features in common. These features can be described by the same mathematics we use when introducing Ampère's law in an introductory physics course. We discuss these common features.

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.

Motion of electrons in liquidH4e

We present theoretical results on the stationary-state motion of electron bubbles in liquid $^{4}\text{H}\text{e}$ both at zero and negative pressures. As the velocity increases, the moving electron bubble is squeezed along the direction of motion while it expands in the transverse directions. When the electron speed is large enough, as a consequence of this change in shape, a vortical fluid motion is induced around the bubble equator which eventually results in the formation and emission of a quantized vortex ring as a critical velocity is reached. This process occurs at zero pressure and at negative pressures down to $\ensuremath{\sim}\ensuremath{-}1.2\text{ }\text{bar}$. Below this value, the bubble becomes unstable and explodes as soon as the critical velocity is reached. Our results show that fast-moving electron bubbles explode in the pressure range where unidentified electron objects have been found to explode in recent cavitation experiments.

Rayleigh-Taylor instability and mushroom-pattern formation in a two-component Bose-Einstein condensate

The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean-field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system.

Vortex rings in classical and quantum systems

The study of vortex rings has been pursued for decades and is a particularly difficult subject. However, the discovery of quantized vortex rings in superfluid helium has greatly increased interest in vortex rings with very thin cores. While rapid progress has been made in the simulation of quantized vortex rings, there has not been comparable progress in laboratory studies of vortex rings in a viscous fluid such as water. This article overviews the history and current frontiers of classical and quantum vortex rings. After introducing the classical results, this review discusses thin-cored vortex rings in superfluid helium in section 2, and recent progress in understanding vortex rings of very thin cores propagating in water in section 3.

Motion of vortex ring with tracer particles in superfluid helium

Recent experiments on quantum turbulence in superfluid helium made use of small tracer particles to track the motion of quantized vortices, determine velocity statistics and visualize vortex reconnections. A problem with this visualization technique is that it may change the turbulent flow which it visualizes. To address this problem, we derive and solve the equations of motion of a quantized vortex ring which contains a given number of particles trapped on the vortex core, hence derive a quantitative criterion to determine in which measure small particles trapped in quantized vortices affect vortex motion. Finally we apply the criterion to a recent experiment.

The Decay of a Quantized Vortex Ring and the Influence of Tracer Particles

We capture the decay of a quantized vortex ring in superfluid helium-4 by imaging particles trapped on the vortex core. The ring shrinks in time, providing direct evidence for the dissipation of energy in the superfluid. The ring with trapped particles collapses more slowly than predicted by an available theory, but the collapse rate can be predicted correctly if the trapping of the particles on the core is taken into account. We theoretically explore the conditions under which particles may be considered passive tracers of quantized vortices and estimate, in particular, that their dynamics on the large-scale is largely unaffected by the burden of trapped particles if the latter are spaced by more than ten particle diameters along the vortex core, at temperatures between 1.5 K and 2.1 K.

Vortex rings in toroidal Bose-Einstein condensates

We study vortex ring solutions of the Gross-Pitaevskii equation for Bose-Einstein condensates confined in toroidal traps. Analogously to the Feynman-Onsager ansatz for a single vortex line, we assume a condensate wavefunction that describes a quantized vortex ring. This leads to a modified Gross-Pitaevskii equation that incorporates vortex ring solutions. By numerically solving this equation, we have obtained the density profiles and the vortex core structure. We have also calculated the nucleation energy of a vortex ring, and have analyzed its dependence on the ring position. Finally, a qualitative description of the vortex ring dynamics is presented.

On superflow in solidHe4

Kim and Chan have recently observed Non-Classical Rotational Inertia (NCRI) for solid $^4$He in Vycor glass, gold film, and bulk. Their low $T$ value of the superfluid fraction, $\rho_{s}/\rho\approx0.015$, is consistent with what is known of the atomic delocalization in this quantum solid. By including a lattice mass density $\rho_{L}$ distinct from the normal fluid density $\rho_{n}$, we argue that $\rho_{s}(T)\approx\rho_{s}(0)-\rho_{n}(T)$, and we develop a model for the normal fluid density $\rho_{n}$ with contributions from longitudinal phonons and ``defectons'' (which dominate). The Bose-Einstein Condensation (BEC) and macroscopic phase inferred from NCRI implies quantum vortex lines and quantum vortex rings, which may explain the unusually low critical velocity and certain hysteretic phenomena.

Intrinsic critical velocities in superfluid4He flow through 12-?m diameter orifices near T?: Experiments on the effect of geometry

We report super fluid4He flow measurements at temperatures from 1.2 K up to Tλ — 3 mK in three orifices of different mesoscopic geometry. Under conditions of our experiments, the flow usually reaches a temperature-dependent intrinsic critical velocity, where dissipation is believed to occur by thermal (or quantum) nucleation of individual quantized vortex rings or loops. The nucleation rate should be sensitive to the wall geometry of the flow channel and to any local velocity enhancement at the most favorable nucleation site. According to the Iordanskii-Langer-Fisher (ILF) theory, the radius of the “critical” vortex ring, the threshold size which can grow freely by extracting energy from the flow, increases inversely as the superfluid density on approach to the superfluid onset temperature, Tλ. Thus sufficiently near Tλ the critical ring should be large enough that the geometry relevant to the nucleation process and local velocity enhancement can be studied by scanning electron microscope (SEM). We examined our three orifices by SEM. One, a standard optical pinhole, has a relatively smooth taper on one side and a sharp lip on the other. The second is similar, but contains a 1-μm flake perpendicular to the flow, which should provide additional velocity enhancement at its edge. In the third, the sharp lip is beveled to reduce the velocity enhancement at that site. Contrary to expectation, the intrinsic critical velocities are the same, within a relative calibration error of 10%, in all three cases. Thus, local sites of enhanced velocity do not appear to be active in nucleating vortices. This raises a question whether the classical two-fluid model which underlies the ILF calculation is adequate to describe the superfluid hydro-dynamics near walls, as it affects the vortex nucleation process.

Anomalous temperature dependence of the vortex nucleation rate due to negative ions in ultradilute superfluid 3He/ 4He solutions

The rate ν at which negative ions create quantized vortex rings in superfluid 3He/ 4He solutions has been measured for temperatures T within 90<T<500mK, for 3He/ 4He isotopic ratios x 3<10 -7 , pressures P within 17<P<25 bar, and electric fields E within 10 2<E<10 6Vm -1 . For fixed P, x 3 and E, it has been found that ν( T) exhibits unexpected sharp local maxima, together with associated small velocity anomalies.

Conservation law for linked cosmic string loops

Taking a cue from the connection between fluid helicity and the linkage between closed vortices in ordinary turbulent flow, we examine topological restrictions on the linkage of cosmic string loops (or superfluid quantum vortex rings). The analog of helicity in these cases vanishes, but loops (and vortex rings) can link together, the extent of linkage (knotting included) being related to the contorsion of the loops or rings by a topological conservation law. This law is respected by intercommunication. One consequence is that total loop contorsion is quantized in integers.

Motion of charged vortex rings in helium II.

We show that an ion carried through an electric field by a quantized vortex ring in helium II will cause a symmetric change in the radius of the ring, even though the ion is located asymmetrically on the core of the vortex ring. The localized force on the ion will combine with a specific series of vortex waves to give a uniform growth of the ring with a small component of drift velocity perpendicular to the applied electric field. This type of energy transfer may also play an important role in superfluid turbulence. Our calculations should be valid for localized forces on thin-core classical vortices as well.