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.

FIG. 3. Calculated equilibrium density profiles of a deformable 4 He cylinder rotating around its symmetry axis at fixed L SF =N He ¼ 7.83ℏ for different numbers of vortices. Streamlines are shown in black. The positions of the vortex cores are marked by red dots for visualization. The color bar shows the density in units of Å −3 .

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

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For more than two decades, encapsulation in superfluid helium nanodroplets has served as a reliable technique for probing the structure and dynamics of molecules and clusters at a low temperature of ≈0.37 K. Due to weak interactions between molecules and the host liquid helium, good spectral resolution can usually be achieved, making helium droplets an ideal matrix for spectroscopy in a wide spectral range from infrared to ultraviolet. Furthermore, rotational structure in the spectra of small molecules provides a unique probe for interactions with the superfluid on an atomic scale. This review presents a summary of results and a discussion of recent experimental developments in helium droplet spectroscopy with the emphasis laid on infrared studies. Initially, studies focused on single molecules and have been expanded to larger species, such as metal-molecular clusters, biomolecules, free radicals, ions, and proteins. ARTICLE HISTORY

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

Lensless x-ray microscopy requires the recovery of the phase of the radiation scattered from a specimen. Here, we demonstrate a de novo phase retrieval technique by encapsulating an object in a superfluid helium nanodroplet, which provides both a physical support and an approximate scattering phase for the iterative image reconstruction. The technique is robust, fast-converging, and yields the complex density of the immersed object. Images of xenon clusters embedded in superfluid helium droplets reveal transient configurations of quantum vortices in this fragile system.

Previous single-pulse extreme ultraviolet and x-ray coherent diffraction studies revealed that superfluid 4 He droplets obtained in a free jet expansion acquire sizable angular momentum, resulting in significant centrifugal distortion. Similar experiments with normal fluid 3 He droplets may help elucidate the origin of the large degree of rotational excitation and highlight similarities and differences of dynamics in normal and superfluid droplets. Here, we present a comparison of the shapes of isolated 3 He and 4 He droplets following expansion of the corresponding fluids in vacuum at temperatures as low as ∼2 K. Large 3 He and 4 He droplets with average radii of ∼160 and ∼350 nm, respectively, were produced. We find that the majority of the shapes of 3 He droplets in the beam correspond to rotating oblate spheroids, in agreement with previous observations for 4 He droplets. The aspect ratio of the droplets is related to the degree of their rotational excitation, which is discussed in terms of reduced angular momenta () and reduced angular velocities (), the average values of which are found to be similar in both isotopes. This similarity suggests that comparable mechanisms induce rotation regardless of the isotope. We hypothesize that the observed distribution of droplet sizes and angular momenta originates from processes in the dense region close to the nozzle, where a significant velocity spread and frequent collisions between droplets induces excessive rotation followed by droplet fission.