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Nucleation of Quantized Vortices from Rotating Superfluid Drops

Russell James Donnelly

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

The long-term goal of this project is to study the nucleation of quantized vortices in helium II by investigating the behavior of rotating droplets of helium II in a reduced gravity environment. The objective of this ground-based research grant was to develop new experimental techniques to aid in accomplishing that goal. The development of an electrostatic levitator for superfluid helium, described below, and the successful suspension of charged superfluid drops in modest electric fields was the primary focus of this work. Other key technologies of general low temperature use were developed and are also discussed.

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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.

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Superfluid helium droplets represent a unique state of matter, which are large clusters of helium typically containing approximately 103-1011 helium atoms and exhibit remarkable properties such as superfluidity, a very low temperature (0.37 K) and high thermal conductivity. This PhD project investigates two novel aspects of superfluid helium droplets: the use of superfluid helium nanodroplets as the nanoreactors to grow magnetic nanoparticles and the generation and exploration of quantum vortices in a controlled manner. In the first part, we exploit the very low temperature and rapid cooling to develop a new approach for fabricating magnetic nanoparticles. For the very low temperature and the ultrahigh thermal conductivity, superfluid helium can suppress thermal effects during the atom-by-atom growth of magnetic nanoparticles, making the relatively weak exchange interactions (compared with metallic bonding) the driving force. As a result, the atomic spins align for ferromagnetic elements and thus the magnetic moments of nanoparticles are maximized. In particular, we focus on iron nanoparticles coated by a gold shell and investigate their properties by electron microscopy (for structural investigation) and x-ray circular dichroism (XMCD), for magnetic property measurement) at the Diamond Light Source. We first study mass spectrometry of small iron clusters and observed abnormal behaviours. Unlike other molecular clusters formed in helium droplets such as water, gold and silver, which typically follow a Poisson distribution, Fe+ channel was found to be far greater than that of FeN+ (N = 2-8) clusters. We postulate this as an indicator for the formation of high-spin iron clusters inside superfluid helium and attempt to provide an interpretation based on DFT calculations. However, XMCD showed an expected low magnetisation for Fe/Au core-shell nanoparticles which is even lower than iron oxide nanoparticles, indicating that the neutral Fe atoms are oxidized into Fe2+ within the nanoparticles which is magnetically inert. This is accounted by the very high electron negativity of Au atoms and the alloying effect during the growth of nanoparticles, which dismisses the magnetic properties. Our work shows that the choice of protective shell is important to maintain the magnetic properties of iron nanoparticles and points the direction for the next-step research. The second part presents a breakthrough in quantum vortex research. We demonstrate a novel method for generating controlled vortex arrays in superfluid helium droplets through collisions with cesium ions. Subsequential addition of metal atoms (Ag and Au) to helium droplets and the formation of nanodroplets allow the vortex lattices to be imaged after the nanoparticles are deposited onto a solid surface. By this approach we have revealed a record-high vortex density of 5.6×10¹⁴ m⁻², exceeding previous observations in bulk superfluid helium by more than six orders of magnitude. This unprecedented vortex density opens new possibilities for studying quantum hydrodynamics at extreme angular momenta and investigating quantum turbulence in previously inaccessible regimes. Through detailed theoretical analysis and experimental characterization, this work establishes superfluid helium droplets as a versatile platform for both materials synthesis and fundamental research. Our findings not only advance the understanding of superfluidity but also provide a new pathway for developing high-performance magnetic nanomaterials that can potentially revolutionize biomedical science and technologies.

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Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].

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Journal of Physics Conference Series•Mar 21, 2006•10 citations
The long-term goal of this project is to study the nucleation of quantized vortices in helium II by investigating the behavior of rotating droplets of helium II in a reduced gravity environment. The objective of this ground-based research grant was to develop new experimental techniques to aid in accomplishing that goal. The development of an electrostatic levitator for superfluid helium, described below, and the successful suspension of charged superfluid drops in modest electric fields was the primary focus of this work. Other key technologies of general low temperature use were developed and are also discussed.
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.
Superfluid helium droplets represent a unique state of matter, which are large clusters of helium typically containing approximately 103-1011 helium atoms and exhibit remarkable properties such as superfluidity, a very low temperature (0.37 K) and high thermal conductivity. This PhD project investigates two novel aspects of superfluid helium droplets: the use of superfluid helium nanodroplets as the nanoreactors to grow magnetic nanoparticles and the generation and exploration of quantum vortices in a controlled manner. In the first part, we exploit the very low temperature and rapid cooling to develop a new approach for fabricating magnetic nanoparticles. For the very low temperature and the ultrahigh thermal conductivity, superfluid helium can suppress thermal effects during the atom-by-atom growth of magnetic nanoparticles, making the relatively weak exchange interactions (compared with metallic bonding) the driving force. As a result, the atomic spins align for ferromagnetic elements and thus the magnetic moments of nanoparticles are maximized. In particular, we focus on iron nanoparticles coated by a gold shell and investigate their properties by electron microscopy (for structural investigation) and x-ray circular dichroism (XMCD), for magnetic property measurement) at the Diamond Light Source. We first study mass spectrometry of small iron clusters and observed abnormal behaviours. Unlike other molecular clusters formed in helium droplets such as water, gold and silver, which typically follow a Poisson distribution, Fe+ channel was found to be far greater than that of FeN+ (N = 2-8) clusters. We postulate this as an indicator for the formation of high-spin iron clusters inside superfluid helium and attempt to provide an interpretation based on DFT calculations. However, XMCD showed an expected low magnetisation for Fe/Au core-shell nanoparticles which is even lower than iron oxide nanoparticles, indicating that the neutral Fe atoms are oxidized into Fe2+ within the nanoparticles which is magnetically inert. This is accounted by the very high electron negativity of Au atoms and the alloying effect during the growth of nanoparticles, which dismisses the magnetic properties. Our work shows that the choice of protective shell is important to maintain the magnetic properties of iron nanoparticles and points the direction for the next-step research. The second part presents a breakthrough in quantum vortex research. We demonstrate a novel method for generating controlled vortex arrays in superfluid helium droplets through collisions with cesium ions. Subsequential addition of metal atoms (Ag and Au) to helium droplets and the formation of nanodroplets allow the vortex lattices to be imaged after the nanoparticles are deposited onto a solid surface. By this approach we have revealed a record-high vortex density of 5.6×10¹⁴ m⁻², exceeding previous observations in bulk superfluid helium by more than six orders of magnitude. This unprecedented vortex density opens new possibilities for studying quantum hydrodynamics at extreme angular momenta and investigating quantum turbulence in previously inaccessible regimes. Through detailed theoretical analysis and experimental characterization, this work establishes superfluid helium droplets as a versatile platform for both materials synthesis and fundamental research. Our findings not only advance the understanding of superfluidity but also provide a new pathway for developing high-performance magnetic nanomaterials that can potentially revolutionize biomedical science and technologies.
Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].
This project focused mainly on the fabrication and characterisation of atomic clusters, molecular clusters and nanostructures made with the aid of helium droplets. Nanoparticles with different sizes have been fabricated by controlling the droplet source expansion conditions. Large silver nanoparticles with both spherical and non-spherical shapes were produced successfully using Cs+ ion as a seeding agent in helium droplets. Self-assembled nanostructures constructed with well-defined distances has also been achieved using organic molecules as structural templates.\nIn addition to particles, nanowires were also investigated. The growth of nanowires is thought to derive from quantized vortices inside large helium droplets. Quantized vortices can act as an aligning tool for one-dimensional growth. TEM images from particle deposition have provided the first experimental evidence that multiply quantized vortices might exist in large helium droplets formed at the edge of helium droplet expansion due to the faster rotation in the helium droplets formed at that position.\nFinally, in this project we have fabricated, for the first time, binary metal/semiconductor nanoparticles and nanowires by the sequential addition of metal and then CdS to a helium droplet. The formation of Au/CdS core-shell nanowires was confirmed through the crystalline structures of the core and shell regions using High Resolution Transmission Electron Microscopy (HRTEM) images.