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.

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.

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.

The utility of a continuous beam of He droplets for the assembly and surface deposition of Ag N clusters, ~ 300 -6 000, is studied with transmission electron microscopy. Images of the clusters on amorphous carbon substrates obtained at short deposition times have provided for a measure of the size distribution of the metal clusters. The average sizes of the deposited clusters are in good agreement with an energy balance based estimate of Ag N cluster growth in He droplets. Measurements of the deposition rate indicate that upon impact with the surface the Heembedded cluster is attached with high probability. The stability of the deposited clusters on the substrate is discussed.

Ag(N) clusters with up to thousands of atoms were grown in large He droplets and studied by optical spectroscopy. For N≲10(3) the spectra are dominated by a surface plasmon resonance near 3.8 eV and a broad feature in the UV, consistent with absorption by individual metallic particles. Larger clusters reveal unexpectedly strong broad absorption at low frequencies, extending down to ≈0.5 eV. This suggests a transition from single-center to multicenter formation, in agreement with estimates of cluster growth kinetics in He droplets. Moreover, the spectra of large clusters develop a characteristic dispersion profile at 3.5-4.5 eV, indicative of the coexistence of localized and delocalized electronic excitations in composite clusters, as predicted theoretically.

Here, we have studied the utility of large He droplets of 10(5)-10(7) atoms for the growth of composite clusters consisting of an Ag core and a shell of ethane molecules. The clusters have been assembled by doping He droplets with up to 10(3) Ag atoms and ethane molecules in two sequential pickup cells and studied via infrared spectroscopy in the C-H stretch region of the ethane molecules. We found that the ν7 band of ethane molecules at the interface with the Ag atoms has a low frequency shift of approximately 15 cm(-1) with respect to that of more distant ethane molecules away from the interface. The intensity ratio of the two bands was used for evaluation of the Ag core and ethane shell cluster structure. We found that the number of surface ethane molecules is in good agreement with a model that assumes a dense, core-shell structure for clusters containing less than about 100 atoms. However, large Ag clusters consisting of about 3000 atoms have a factor of about 5 larger surface area than that predicted by the model, indicating a ramified structure for such larger Ag clusters obtained in liquid He. Moreover, we demonstrate that He droplets behave as calorimeters for measurements of the number of captured atoms and molecules as well as the amount of absorbed laser energy.

Rotating superfluid He droplets of approximately 1 μm in diameter were obtained in a free nozzle beam expansion of liquid He in vacuum and were studied by single-shot coherent diffractive imaging using an x-ray free electron laser. The formation of strongly deformed droplets is evidenced by large anisotropies and intensity anomalies (streaks) in the obtained diffraction images. The analysis of the images shows that, in addition to previously described axially symmetric oblate shapes, some droplets exhibit prolate shapes. Forward modeling of the diffraction images indicates that the shapes of rotating superfluid droplets are very similar to their classical counterparts, giving direct access to the droplet angular momenta and angular velocities. The analyses of the radial intensity distribution and appearance statistics of the anisotropic images confirm the existence of oblate metastable superfluid droplets with large angular momenta beyond the classical bifurcation threshold.3

Single He nanodroplets doped with Xe atoms are studied via ultrafast coherent x-ray diffraction imaging. The diffraction images show that rotating He nanodroplets about 200 nm in diameter contain a small number of symmetrically arranged quantum vortices decorated with Xe clusters. Unexpected large distances of the vortices from the droplet center (≈0.7–0.8 droplet radii) are explained by a significant contribution of the Xe dopants to the total angular momentum of the droplets and a stabilization of widely spaced vortex configurations by the trapped Xe clusters