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arXiv:1308.6171 · Physical Review Letters

Reconnections of Quantized Vortex Rings in Superfluid He4 at Very Low Temperatures

Paul M. Walmsley, P. A. Tompsett, D. E. Zmeev, Andrei I. Golov

Published Sep 17, 2014• 21 citations
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Abstract

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.

DOI
10.1103/physrevlett.113.125302

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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.
Motions of vortices are fundamental characteristics of quantum turbulence. These motions are expected to be governed only by quantized circulations in superfluids at the zero temperature limit. In the present paper, we report the motions of vortex rings emitted from a quantum turbulence in superfluid 4 He, by detecting vortex rings using a vortex-free vibrating wire as a detector. The time of flights of vortex rings are distributed, because vortex rings are emitted in any direction from a turbulent region and the detector can respond only to a reachable vortex ring. By measuring time-of-flights many times, we find an exponential distribution of time-of-flights with a non-detection period, which corresponds to the fastest time of flights of vortex rings. For a larger generation power of vortex rings, a distribution of time-of-flights still shows a single exponential distribution, but a non-detection period becomes shorter. This result implies that sizes of emitted vortex rings are distributed dependently on the generation power of turbulence. The observed exponential distributions are confirmed by numerical simulations of the dynamics of vortex rings.
An oscillating object can stretch quantized vortices attached to it in superfluids due to the relative superflow, steadily generating quantum turbulence, even in the zero-temperature limit. We report the emission and propagation of quantized vortices from quantum turbulence generated in superfluid 4{}^{4}4He at low temperatures. A vortex-free vibrating wire enables us to detect the first collision of vortex rings and therefore to measure the time-of-flight of a vortex emitted from a generator to a detector. The detection times from the start of turbulence generation exhibit an exponential distribution, suggesting that the detection is a Poisson process. Vortices are emitted continuously, but each vortex has a random flight velocity and direction. We estimated the nondetection time and mean detection period from the distribution for two flight distances. By estimating the flight velocity, we find that only vortices with velocities lower than the detector velocity can be detected, even if the sizes of the emitted vortices are smaller than the wire thickness or the vibration amplitude. The ratio of the detection rate as a function of vortex velocity suggests anisotropic emission of vortices from the quantum turbulence.
We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40 m/s, respectively, induced by the long-range van der Waals attraction between the droplets.
Reconnections between quantum vortex filaments in the presence of trapped particles are investigated using numerical simulations of the Gross-Pitaevskii equation. Particles are described with classical degrees of freedom and modeled as highly repulsive potentials which deplete the superfluid. First, the case of a vortex dipole with a single particle trapped inside one of the vortices is studied. It is shown that the reconnection takes place at the position of the particle as a consequence of the symmetry breaking induced by it. The separation rate between the reconnecting points is compatible with the known dynamics of quantum vortex reconnections, and it is independent of the particle mass and size. After the reconnection, the particle is pushed away with a constant velocity, and its trajectory is deflected because of the transverse momentum exchange with the vortex filaments. The momentum exchanges between the particle, the vortex, and a density pulse are characterized. Finally, the reconnection of two linked rings, each of them with several initially randomly distributed particles, is studied. It is observed that generically, reconnections take place at the location of trapped particles. It is shown that reconnection dynamics is unaffected for light particles.
We introduce a comprehensive theoretical framework for the fermionic superfluid dynamics, grounded on a local extension of the time-dependent density functional theory. With this approach, we describe the generation and the real-time evolution and interaction of quantized vortices, the large-amplitude collective modes, as well as the loss of superfluidity at high flow velocities. We demonstrate the formation of vortex rings and provide a microscopic description of the crossing and reconnection of quantized vortex lines in a fermion superfluid, which provide the mechanism for the emergence of quantum turbulence at very low temperatures. We observe that superfluidity often survives when these systems are stirred with velocities far exceeding the speed of sound.