Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2110.10612 · Physical review. B./Physical review. B

Merging of superfluid helium nanodroplets with vortices

José María Escartín, Francesco Ancilotto, M. Barranco, Martí Pi

Published Jan 13, 2022• 5 citations
arXivHTMLPDF

Abstract

Within density functional theory, we have investigated the coalescence dynamics of two superfluid helium nanodroplets hosting vortex lines in different relative orientations, which are drawn towards each other by the Van der Waals mutual attraction. We have found a rich phenomenology depending on how the vortex lines are oriented. In particular, when a vortex and antivortex lines are present in the merging droplets, a dark soliton develops at the droplet contact region, which eventually decays into vortex rings. Reconnection events are observed between the vortex lines or rings, leading to the creation of more vortices. Our simulations show the interplay between vortex creation and reconnections, as well as the effect of the droplet surface which pins the vortex ends and, by reflecting short-wavelength excitations produced by the interactions between vortices, strongly affects the droplet final state. Additional vorticity is nucleated in the proximity of surface indentations produced in the course of the dynamics, which in turn interact with other vortices present in the droplets. These effects, obviously absent in the case of bulk liquid helium, show that the droplet surface may act as a multiplier of vortex reconnections. The analysis of the energy spectrum shows that vortex-antivortex ring annihilation, as well as vortex-antivortex reconnections, yields roton bursts of different intensity.

DOI
10.1103/physrevb.105.024511

Related papers

Vorticity and quantum turbulence in the merging of superfluid helium nanodroplets

José María Escartín, Francesco Ancilotto, M. Barranco +1 more

We have studied the merging of two identical $^{4}\mathrm{He}$ droplets at zero temperature, caused by their van der Waals mutual attraction. During the early stages of the merging, density structures appear which closely match the experimental observations by Vicente et al. [J. Low Temp. Phys. 121, 627 (2000)]. When the droplets are merging, quantized vortex-antivortex ring pairs nucleate at the surface and annihilate inside the merged droplet producing a roton burst. We also observe the nucleation of quantized vortex-antivortex rings that wrap the droplet surface and remain localized on the surface until they eventually decay into short-wavelength surface waves. Analysis of the kinetic energy spectrum discloses the existence of a regime where turbulence caused by vortex interaction and annihilation is characterized by a Kolmogorov power law. This is followed by another regime where roton radiation---produced by vortex-antivortex annihilation---dominates, whose hallmark is a weak, turbulent surface dynamics. We suggest that similar processes might appear in superfluid helium droplets after they capture impurities or if they are produced by hydrodynamic instability of a liquid jet. Experiments on collisions between recently discovered self-bound Bose-Einstein condensates should display a similar phenomenology.

arXiv:1902.02747•Physical review. B./Physical review. B•Apr 16, 2019•21 citations

Energetics and possible formation and decay mechanisms of vortices in helium nanodroplets

Kevin K. Lehmann, Roman Schmied

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.

arXiv:cond-mat/0306674•Physical review. B, Condensed matter•Dec 31, 2003•34 citations

Quantized vortex nucleation in collisions of superfluid nanoscopic helium droplets at zero temperature

Ernesto García‐Alfonso, Francesco Ancilotto, M. Barranco +2 more

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.

arXiv:2307.02883•The Journal of Chemical Physics•Aug 21, 2023•1 citation

Shapes and vorticities of superfluid helium nanodroplets

Luis F. Gomez, Ken Ferguson, James Patrick Cryan +41 more

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.

Science•Aug 21, 2014•230 citations

Coexistence of vortex arrays and surface capillary waves in spinning prolate superfluid He4 nanodroplets

Martí Pi, José María Escartín, Francesco Ancilotto +1 more

Within density functional theory, we have studied the interplay between vortex arrays and capillary waves in spinning prolate $^{4}\mathrm{He}$ droplets made of several thousand helium atoms. Surface capillary waves are ubiquitous in prolate superfluid $^{4}\mathrm{He}$ droplets, and depending on the size and angular momentum of the droplet, they may coexist with vortex arrays. We have found that the equilibrium configuration of small prolate droplets is vortex free, evolving towards vortex hosting as the droplet size increases. This result is in agreement with a recent experiment [O'Connell et al., Phys. Rev. Lett. 124, 215301 (2020)] that disclosed that vortex arrays and capillary waves coexist in the equilibrium configuration of very large drops. In contrast to viscous droplets executing rigid-body rotation, the stability phase diagram of spinning $^{4}\mathrm{He}$ droplets cannot be universally described in terms of dimensionless angular momentum and angular velocity variables: Instead, the rotational properties of superfluid helium droplets display a clear dependence on the droplet size and the number of vortices they host.

arXiv:2104.06712•Physical review. B./Physical review. B•Sep 9, 2021•11 citations

Traces of Vortices in Superfluid Helium Droplets

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

We report on the observation of vortices in superfluid $^{4}\mathrm{He}$ 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.

Bulletin of the American Physical Society•Feb 29, 2012•0 citations
Within density functional theory, we have investigated the coalescence dynamics of two superfluid helium nanodroplets hosting vortex lines in different relative orientations, which are drawn towards each other by the Van der Waals mutual attraction. We have found a rich phenomenology depending on how the vortex lines are oriented. In particular, when a vortex and antivortex lines are present in the merging droplets, a dark soliton develops at the droplet contact region, which eventually decays into vortex rings. Reconnection events are observed between the vortex lines or rings, leading to the creation of more vortices. Our simulations show the interplay between vortex creation and reconnections, as well as the effect of the droplet surface which pins the vortex ends and, by reflecting short-wavelength excitations produced by the interactions between vortices, strongly affects the droplet final state. Additional vorticity is nucleated in the proximity of surface indentations produced in the course of the dynamics, which in turn interact with other vortices present in the droplets. These effects, obviously absent in the case of bulk liquid helium, show that the droplet surface may act as a multiplier of vortex reconnections. The analysis of the energy spectrum shows that vortex-antivortex ring annihilation, as well as vortex-antivortex reconnections, yields roton bursts of different intensity.
We have studied the merging of two identical 4He^{4}\mathrm{He}4He droplets at zero temperature, caused by their van der Waals mutual attraction. During the early stages of the merging, density structures appear which closely match the experimental observations by Vicente et al. [J. Low Temp. Phys. 121, 627 (2000)]. When the droplets are merging, quantized vortex-antivortex ring pairs nucleate at the surface and annihilate inside the merged droplet producing a roton burst. We also observe the nucleation of quantized vortex-antivortex rings that wrap the droplet surface and remain localized on the surface until they eventually decay into short-wavelength surface waves. Analysis of the kinetic energy spectrum discloses the existence of a regime where turbulence caused by vortex interaction and annihilation is characterized by a Kolmogorov power law. This is followed by another regime where roton radiation---produced by vortex-antivortex annihilation---dominates, whose hallmark is a weak, turbulent surface dynamics. We suggest that similar processes might appear in superfluid helium droplets after they capture impurities or if they are produced by hydrodynamic instability of a liquid jet. Experiments on collisions between recently discovered self-bound Bose-Einstein condensates should display a similar phenomenology.
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 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.
Within density functional theory, we have studied the interplay between vortex arrays and capillary waves in spinning prolate 4He^{4}\mathrm{He}4He droplets made of several thousand helium atoms. Surface capillary waves are ubiquitous in prolate superfluid 4He^{4}\mathrm{He}4He droplets, and depending on the size and angular momentum of the droplet, they may coexist with vortex arrays. We have found that the equilibrium configuration of small prolate droplets is vortex free, evolving towards vortex hosting as the droplet size increases. This result is in agreement with a recent experiment [O'Connell et al., Phys. Rev. Lett. 124, 215301 (2020)] that disclosed that vortex arrays and capillary waves coexist in the equilibrium configuration of very large drops. In contrast to viscous droplets executing rigid-body rotation, the stability phase diagram of spinning 4He^{4}\mathrm{He}4He droplets cannot be universally described in terms of dimensionless angular momentum and angular velocity variables: Instead, the rotational properties of superfluid helium droplets display a clear dependence on the droplet size and the number of vortices they host.
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.