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Physical Review Letters

Traces of Vortices in Superfluid Helium Droplets

Luis F. Gomez, Evgeny Loginov, Andrey F. Vilesov

Published Apr 10, 2012• 123 citations
Publisher

Abstract

We report on the observation of vortices in superfluid 4He droplets produced in the expansion of liquid He. The vortices were traced by introducing Ag atoms, which clustered along the vortex lines, into the droplets. The Ag clusters were subsequently surface-deposited and imaged via electron microscopy. The prevalence of elongated track-shaped deposits shows that vortices are present in droplets larger than about 300 nm and that their lifetime exceeds a few milliseconds. We discuss the possible formation mechanisms and the stability of the vortices.

DOI
10.1103/physrevlett.108.155302

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Helium Superfluidity When physicists rotate the superfluid 4He, it develops a regular array of tiny whirlpools, called vortices. The same phenomenon should occur in helium droplets half a micrometer in size, but studying individual droplets is tricky. Gomez et al. used x-ray diffraction to deduce the shape of individual rotating droplets and image the resulting vortex patterns, which confirmed the superfluidity of the droplets. They found that superfluid droplets can host a surprising number of vortices and can rotate faster than normal droplets without disintegrating. Science , this issue p. [906][1] [1]: /lookup/doi/10.1126/science.1252395

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We report on the observation of vortices in superfluid 4He droplets produced in the expansion of liquid He. The vortices were traced by introducing Ag atoms, which clustered along the vortex lines, into the droplets. The Ag clusters were subsequently surface-deposited and imaged via electron microscopy. The prevalence of elongated track-shaped deposits shows that vortices are present in droplets larger than about 300 nm and that their lifetime exceeds a few milliseconds. We discuss the possible formation mechanisms and the stability of the vortices.
We report on the observation of vortices in superfluid 4He^{4}\mathrm{He}4He droplets produced in the expansion of liquid He. The vortices were traced by introducing Ag atoms, which clustered along the vortex lines, into the droplets. The Ag clusters were subsequently surface-deposited and imaged via electron microscopy. The prevalence of elongated track-shaped deposits shows that vortices are present in droplets larger than about 300 nm and that their lifetime exceeds a few milliseconds. We discuss the possible formation mechanisms and the stability of the vortices.
Helium nanodroplets are considered ideal model systems to explore quantum hydrodynamics in self-contained, isolated superfluids. However, exploring the dynamic properties of individual droplets is experimentally challenging. In this work, we used single-shot femtosecond x-ray coherent diffractive imaging to investigate the rotation of single, isolated superfluid helium-4 droplets containing ~10(8) to 10(11) atoms. The formation of quantum vortex lattices inside the droplets is confirmed by observing characteristic Bragg patterns from xenon clusters trapped in the vortex cores. The vortex densities are up to five orders of magnitude larger than those observed in bulk liquid helium. The droplets exhibit large centrifugal deformations but retain axially symmetric shapes at angular velocities well beyond the stability range of viscous classical droplets.
Free superfluid helium droplets constitute a versatile medium for a diverse range of experiments in physics and chemistry that extend from studies of the fundamental laws of superfluid motion to the synthesis of novel nanomaterials. In particular, the emergence of quantum vortices in rotating helium droplets is one of the most dramatic hallmarks of superfluidity and gives detailed access to the wave function describing the quantum liquid. This review provides an introduction to quantum vorticity in helium droplets, followed by a historical account of experiments on vortex visualization in bulk superfluid helium and a more detailed discussion of recent advances in the study of the rotational motion of isolated, nano- to micrometer-scale superfluid helium droplets. Ultrafast X-ray and extreme ultraviolet scattering techniques enabled by X-ray free-electron lasers and high-order harmonic generation in particular have facilitated the in situ detection of droplet shapes and the imaging of vortex structures inside individual, isolated droplets. New applications of helium droplets ranging from studies of quantum phase separations to mechanisms of low-temperature aggregation are discussed.
Though vortices are an unavoidable presence in bulk superfluid helium, they have not been observed to date in helium nanodroplets. The energy and angular momentum of both straight and curved vortex states of a helium nanodroplet are examined as a function of droplet size. For droplets in the size range of many experiments, it is found that during the pickup of heavy solutes, a significant fraction of events deposit sufficient energy and angular momentum to form a straight vortex line. Curved vortex lines exist down to nearly zero angular momentum and energy, and thus could in principle form in almost any collision. Further, the coalescence of smaller droplets during the cooling by expansion could also deposit sufficient angular momentum to form vortex lines. Despite their high energy, most vortices are predicted to be stable at the final temperature (0.38 K) of helium nanodroplets due to lack of decay channels that conserve both energy and angular momentum.
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.
Helium Superfluidity When physicists rotate the superfluid 4He, it develops a regular array of tiny whirlpools, called vortices. The same phenomenon should occur in helium droplets half a micrometer in size, but studying individual droplets is tricky. Gomez et al. used x-ray diffraction to deduce the shape of individual rotating droplets and image the resulting vortex patterns, which confirmed the superfluidity of the droplets. They found that superfluid droplets can host a surprising number of vortices and can rotate faster than normal droplets without disintegrating. Science , this issue p. [906][1] [1]: /lookup/doi/10.1126/science.1252395