Generation of Large Vortex-Free Superfluid Helium Nanodroplets

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.

Three-dimensional femtosecond snapshots of isolated faceted nanostructures

The structure and dynamics of isolated nanosamples in free flight can be directly visualized via single-shot coherent diffractive imaging using the intense and short pulses of x-ray free-electron lasers. Wide-angle scattering images encode three-dimensional (3D) morphological information of the samples, but its retrieval remains a challenge. Up to now, effective 3D morphology reconstructions from single shots were only achieved via fitting with highly constrained models, requiring a priori knowledge about possible geometries. Here, we present a much more generic imaging approach. Relying on a model that allows for any sample morphology described by a convex polyhedron, we reconstruct wide-angle diffraction patterns from individual silver nanoparticles. In addition to known structural motives with high symmetries, we retrieve imperfect shapes and agglomerates that were not previously accessible. Our results open unexplored routes toward true 3D structure determination of single nanoparticles and, ultimately, 3D movies of ultrafast nanoscale dynamics.

Finding the semantic similarity in single-particle diffraction images using self-supervised contrastive projection learning

Single-shot coherent diffraction imaging of isolated nanosized particles has seen remarkable success in recent years, yielding in-situ measurements with ultra-high spatial and temporal resolution. The progress of high-repetition-rate sources for intense X-ray pulses has further enabled recording datasets containing millions of diffraction images, which are needed for the structure determination of specimens with greater structural variety and dynamic experiments. The size of the datasets, however, represents a monumental problem for their analysis. Here, we present an automatized approach for finding semantic similarities in coherent diffraction images without relying on human expert labeling. By introducing the concept of projection learning, we extend self-supervised contrastive learning to the context of coherent diffraction imaging and achieve a dimensionality reduction producing semantically meaningful embeddings that align with physical intuition. The method yields substantial improvements compared to previous approaches, paving the way toward real-time and large-scale analysis of coherent diffraction experiments at X-ray free-electron lasers.

The Scatman: an approximate method for fast wide-angle scattering simulations

A fast method for wide-angle coherent scattering simulations of weakly absorbing isolated samples, called the Scatman, is presented. Its quantitative agreement with exact solutions and the low simulation time of its software implementation PyScatman open new perspectives for single-shot 3D coherent diffraction imaging.

Single-shot coherent diffraction imaging (CDI) is a powerful approach to characterize the structure and dynamics of isolated nanoscale objects such as single viruses, aerosols, nanocrystals and droplets. Using X-ray wavelengths, the diffraction images in CDI experiments usually cover only small scattering angles of a few degrees. These small-angle patterns represent the magnitude of the Fourier transform of the 2D projection of the sample’s electron density, which can be reconstructed efficiently but lacks any depth information. In cases where the diffracted signal can be measured up to scattering angles exceeding ∼10°, i.e. in the wide-angle regime, some 3D morphological information of the target is contained in a single-shot diffraction pattern. However, the extraction of the 3D structural information is no longer straightforward and defines the key challenge in wide-angle CDI. So far, the most convenient approach relies on iterative forward fitting of the scattering pattern using scattering simulations. Here the Scatman is presented, an approximate and fast numerical tool for the simulation and iterative fitting of wide-angle scattering images of isolated samples. Furthermore, the open-source software implementation of the Scatman algorithm, PyScatman, is published and described in detail. The Scatman approach, which has already been applied in previous work for forward-fitting-based shape retrieval, adopts the multi-slice Fourier transform method. The effects of optical properties are partially included, yielding quantitative results for small, isolated and weakly interacting samples. PyScatman is capable of computing wide-angle scattering patterns in a few milliseconds even on consumer-level computing hardware, potentially enabling new data analysis schemes for wide-angle coherent diffraction experiments.

Deep neural networks for classifying complex features in diffraction images

Intense short-wavelength pulses from free-electron lasers and high-harmonic-generation sources enable diffractive imaging of individual nanosized objects with a single x-ray laser shot. The enormous data sets with up to several million diffraction patterns present a severe problem for data analysis because of the high dimensionality of imaging data. Feature recognition and selection is a crucial step to reduce the dimensionality. Usually, custom-made algorithms are developed at a considerable effort to approximate the particular features connected to an individual specimen, but because they face different experimental conditions, these approaches do not generalize well. On the other hand, deep neural networks are the principal instrument for today's revolution in automated image recognition, a development that has not been adapted to its full potential for data analysis in science. We recently published [Langbehn et al., Phys. Rev. Lett. 121, 255301 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.255301] the application of a deep neural network as a feature extractor for wide-angle diffraction images of helium nanodroplets. Here we present the setup, our modifications, and the training process of the deep neural network for diffraction image classification and its systematic bench marking. We find that deep neural networks significantly outperform previous attempts for sorting and classifying complex diffraction patterns and are a significant improvement for the much-needed assistance during postprocessing of large amounts of experimental coherent diffraction imaging data.

Three-Dimensional Shapes of Spinning Helium Nanodroplets

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.

XUV double-pulses with femtosecond to 650 ps separation from a multilayer-mirror-based split-and-delay unit at FLASH

Extreme ultraviolet (XUV) and X-ray free-electron lasers enable new scientific opportunities. Their ultra-intense coherent femtosecond pulses give unprecedented access to the structure of undepositable nanoscale objects and to transient states of highly excited matter. In order to probe the ultrafast complex light-induced dynamics on the relevant time scales, the multi-purpose end-station CAMP at the free-electron laser FLASH has been complemented by the novel multilayer-mirror-based split-and-delay unit DESC (DElay Stage for CAMP) for time-resolved experiments. XUV double-pulses with delays adjustable from zero femtoseconds up to 650 picoseconds are generated by reflecting under near-normal incidence, exceeding the time range accessible with existing XUV split-and-delay units. Procedures to establish temporal and spatial overlap of the two pulses in CAMP are presented, with emphasis on the optimization of the spatial overlap at long time-delays via time-dependent features, for example in ion spectra of atomic clusters.

Magnetic moments of chromium-doped gold clusters: the Anderson impurity model in finite systems

The magnetic moment of a single impurity atom in a finite free electron gas is studied in a combined x-ray magnetic circular dichroism spectroscopy, charge transfer multiplet calculation, and density functional theory study of size-selected free chromium-doped gold clusters. The observed size dependence of the local magnetic moment can be understood as a transition from a local moment to a mixed valence regime. This shows that the Anderson impurity model essentially describes finite systems even though the discrete density of states introduces a significant deviation from a bulk metal, and the free electron gas is only formed by less than 10 electrons. Electronic shell closure in the gold host minimizes the interaction of localized impurity states with the confined free electron gas and preserves the magnetic moment of 5 μ_{B} fully in CrAu_{2}^{+} and almost fully in CrAu_{6}^{+}. Even for open-shell species, large local moments are observed that scale with the energy gap of the gold cluster. This indicates that an energy gap in the free electron gas stabilizes the local magnetic moment of the impurity atom.