© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

The Journal of Chemical Physics

Sizes of pure and doped helium droplets from single shot x-ray imaging

Rico Mayro P. Tanyag, Camila Bacellar, Weiwu Pang, Charles Bernando, Luis F. Gomez, Curtis F. Jones, Ken Ferguson, Justin Kwok, Denis Anielski, A. Belkacem, Rebecca Boll, John D. Bozek, S. Carron, Gang Chen, Tjark Delmas, Lars Englert, Sascha W. Epp, Benjamin Erk, L. Foucar, Robert Hartmann, Alexander Hexemer, Martin Huth, Stephen R. Leone, H. Jonathan, Stefano Marchesini, Daniel M. Neumark, Billy K. Poon, James S. Prell, Daniel Rolles, Benedikt Rudek, Artem Rudenko, Martin T. Seifrid, Michele L. Swiggers, J. Ullrich, Fabian Weise, Petrus H. Zwart, Christoph Bostedt, Oliver Geßner, Andrey F. Vilesov

Published Jan 7, 2022• 7 citations

Abstract

Advancements in x-ray free-electron lasers on producing ultrashort, ultrabright, and coherent x-ray pulses enable single-shot imaging of fragile nanostructures, such as superfluid helium droplets. This imaging technique gives unique access to the sizes and shapes of individual droplets. In the past, such droplet characteristics have only been indirectly inferred by ensemble averaging techniques. Here, we report on the size distributions of both pure and doped droplets collected from single-shot x-ray imaging and produced from the free-jet expansion of helium through a 5 μm diameter nozzle at 20 bars and nozzle temperatures ranging from 4.2 to 9 K. This work extends the measurement of large helium nanodroplets containing 109–1011 atoms, which are shown to follow an exponential size distribution. Additionally, we demonstrate that the size distributions of the doped droplets follow those of the pure droplets at the same stagnation condition but with smaller average sizes.

DOI: 10.1063/5.0080342

Related papers

Generation of Large Vortex-Free Superfluid Helium Nanodroplets

Anatoli Ulmer, Andrea Heilrath, Björn Senfftleben +38 more

Superfluid helium nanodroplets are an ideal environment for the formation of metastable, self-organized dopant nanostructures. However, the presence of vortices often hinders their formation. Here, we demonstrate the generation of vortex-free helium nanodroplets and explore the size range in which they can be produced. From x-ray diffraction images of xenon-doped droplets, we identify that single compact structures, assigned to vortex-free aggregation, prevail up to 10^{8} atoms per droplet. This finding builds the basis for exploring the assembly of far-from-equilibrium nanostructures at low temperatures.

Physical Review Letters•Aug 16, 2023•11 citations

Three-Dimensional Shapes of Spinning Helium Nanodroplets

Bruno Langbehn, Katharina Sander, Yevheniy Ovcharenko +23 more

A significant fraction of superfluid helium nanodroplets produced in a free-jet expansion has been observed to gain high angular momentum resulting in large centrifugal deformation. We measured single-shot diffraction patterns of individual rotating helium nanodroplets up to large scattering angles using intense extreme ultraviolet light pulses from the FERMI free-electron laser. Distinct asymmetric features in the wide-angle diffraction patterns enable the unique and systematic identification of the three-dimensional droplet shapes. The analysis of a large data set allows us to follow the evolution from axisymmetric oblate to triaxial prolate and two-lobed droplets. We find that the shapes of spinning superfluid helium droplets exhibit the same stages as classical rotating droplets while the previously reported metastable, oblate shapes of quantum droplets are not observed. Our three-dimensional analysis represents a valuable landmark for clarifying the interrelation between morphology and superfluidity on the nanometer scale.

arXiv:1802.10584•Physical Review Letters•Dec 17, 2018•64 citations

Generation of Large Vortex-Free Superfluid Helium Nanodroplets

Anatoli Ulmer, Andrea Heilrath, Björn Senfftleben +38 more

Superfluid helium nanodroplets are an ideal environment for the formation of metastable, self-organized dopant nanostructures. However, the presence of vortices often hinders their formation. Here, we demonstrate the generation of vortex-free helium nanodroplets and explore the size range in which they can be produced. From x-ray diffraction images of xenon-doped droplets, we identify that single compact structures, assigned to vortex-free aggregation, prevail up to $10^8$ atoms per droplet. This finding builds the basis for exploring the assembly of far-from-equilibrium nanostructures at low temperatures.

arXiv:2302.07355•Feb 14, 2023•2 citations

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

Controlled growth of helium nanodroplets from a pulsed source

Shengfu Yang, Scott M. Brereton, Andrew M. Ellis

Factors affecting the size of liquid-helium droplets produced by a pulsed nozzle are described. The shape of the nozzle orifice is found to be important in allowing control of the size of the droplets. With an appropriate choice of nozzle geometry, the average droplet size is shown to be continuously variable over nearly two orders of magnitude by adjustment of the helium gas stagnation pressure and/or temperature. A scaling law similar to, but not identical with, that found for helium droplets produced by continuous supersonic expansion sources is found for the pulsed source. The pulsed nozzle described in this article has been used to make helium droplets ranging in size from a few thousand atoms up to nearly 105 helium atoms.

Review of Scientific Instruments•Oct 1, 2005•32 citations

Sizes of large He droplets

Luis F. Gomez, Evgeny Loginov, Russell Sliter +1 more

Helium droplets spanning a wide size range, N(He) = 10(3)-10(10), were formed in a continuous-nozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the droplet beam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N(He) = 10(5)-10(7). Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10(7)-10(10) atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the droplet beam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He(4) (+) signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N(He) = 10(4)-10(9) atoms.

The Journal of Chemical Physics•Oct 18, 2011•180 citations

Advancements in x-ray free-electron lasers on producing ultrashort, ultrabright, and coherent x-ray pulses enable single-shot imaging of fragile nanostructures, such as superfluid helium droplets. This imaging technique gives unique access to the sizes and shapes of individual droplets. In the past, such droplet characteristics have only been indirectly inferred by ensemble averaging techniques. Here, we report on the size distributions of both pure and doped droplets collected from single-shot x-ray imaging and produced from the free-jet expansion of helium through a 5 μm diameter nozzle at 20 bars and nozzle temperatures ranging from 4.2 to 9 K. This work extends the measurement of large helium nanodroplets containing 109–1011 atoms, which are shown to follow an exponential size distribution. Additionally, we demonstrate that the size distributions of the doped droplets follow those of the pure droplets at the same stagnation condition but with smaller average sizes.

Superfluid helium nanodroplets are an ideal environment for the formation of metastable, self-organized dopant nanostructures. However, the presence of vortices often hinders their formation. Here, we demonstrate the generation of vortex-free helium nanodroplets and explore the size range in which they can be produced. From x-ray diffraction images of xenon-doped droplets, we identify that single compact structures, assigned to vortex-free aggregation, prevail up to 10^{8} atoms per droplet. This finding builds the basis for exploring the assembly of far-from-equilibrium nanostructures at low temperatures.

A significant fraction of superfluid helium nanodroplets produced in a free-jet expansion has been observed to gain high angular momentum resulting in large centrifugal deformation. We measured single-shot diffraction patterns of individual rotating helium nanodroplets up to large scattering angles using intense extreme ultraviolet light pulses from the FERMI free-electron laser. Distinct asymmetric features in the wide-angle diffraction patterns enable the unique and systematic identification of the three-dimensional droplet shapes. The analysis of a large data set allows us to follow the evolution from axisymmetric oblate to triaxial prolate and two-lobed droplets. We find that the shapes of spinning superfluid helium droplets exhibit the same stages as classical rotating droplets while the previously reported metastable, oblate shapes of quantum droplets are not observed. Our three-dimensional analysis represents a valuable landmark for clarifying the interrelation between morphology and superfluidity on the nanometer scale.

Superfluid helium nanodroplets are an ideal environment for the formation of metastable, self-organized dopant nanostructures. However, the presence of vortices often hinders their formation. Here, we demonstrate the generation of vortex-free helium nanodroplets and explore the size range in which they can be produced. From x-ray diffraction images of xenon-doped droplets, we identify that single compact structures, assigned to vortex-free aggregation, prevail up to

10^8

atoms per droplet. This finding builds the basis for exploring the assembly of far-from-equilibrium nanostructures at low temperatures.

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.

Factors affecting the size of liquid-helium droplets produced by a pulsed nozzle are described. The shape of the nozzle orifice is found to be important in allowing control of the size of the droplets. With an appropriate choice of nozzle geometry, the average droplet size is shown to be continuously variable over nearly two orders of magnitude by adjustment of the helium gas stagnation pressure and/or temperature. A scaling law similar to, but not identical with, that found for helium droplets produced by continuous supersonic expansion sources is found for the pulsed source. The pulsed nozzle described in this article has been used to make helium droplets ranging in size from a few thousand atoms up to nearly 105 helium atoms.

Helium droplets spanning a wide size range, N(He) = 10(3)-10(10), were formed in a continuous-nozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the droplet beam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N(He) = 10(5)-10(7). Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10(7)-10(10) atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the droplet beam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He(4) (+) signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N(He) = 10(4)-10(9) atoms.