The complex refractive index of a material governs its light-matter interactions, with intense light fields enabling tailored nonlinear optical responses. In the X-ray regime, rapid photoionization limits the potential of nonlinear techniques by inducing irreversible electronic damage. Here we demonstrate that intense, sub-femtosecond X-ray pulses, shorter than typical Auger decay times, can partially reverse photoexcitation via stimulated emission near atomic resonances. By analyzing thousands of coherent diffraction patterns and ion spectra from neon nanoparticles exposed to sub-fs and 15-fs pulses, we observe enhanced X-ray diffraction alongside reduced energy absorption for sub-fs pulses. Theoretical modeling attributes this to dynamics akin to Rabi flopping that prolong the lifetime of resonant states and suppress electronic bleaching. These findings suggest that ultrashort, intense X-ray pulses enable active control of X-ray refractive index and damage pathways, opening avenues for improved high-resolution imaging and nonlinear spectroscopy in complex nanoscale systems.

We experimentally demonstrate that pairs of time-delayed ultrabright and ultrashort X-ray pulses of two different colors, delivered by modern X-ray Free Electron Lasers, can provide two time-delayed snapshots of a sample. We introduce Dichography, a method that algorithmically separates the diffraction signals overlapping on the detector and independently retrieves the two images of the specimen. We employ Dichography to reconstruct two views of individual xenon-doped helium nanodroplets with 20 nm spatial resolution. The consistency of structures observed in both images at delays up to 750 fs provides evidence that, under these illumination conditions, significant structural damage only occurs at longer timescales. We further validate the method by imaging pairs of silver nanoparticles intercepted by the same light pulse. Dichography enables a new class of experiments across physics, chemistry, and materials science, making a significant step toward the original promise of X-ray free-electron lasers to capture ultrafast movies of nanomatter.

Two-color X-ray imaging with Free Electron Laser pulses offers a powerful approach for probing ultrafast structural dynamics in nanoscale systems, combining (near-)atomic spatial resolution with femtosecond temporal precision. The first X-ray pulse captures the object’s initial state, while the second, time-delayed pulse records its subsequent evolution. A key challenge lies in disentangling the two patterns simultaneously recorded by the same detector. We demonstrate the realization of this approach on structurally varying nanoscale particles using two X-ray pulses of different photon energies, 1 and 1.2 keV. Sub-micrometer helium nanodroplets generated in vacuum are irradiated by the two X-ray pulses separated in time by up to 750 femtoseconds. Taking advantage of the high photon-energy resolution of the imaging detector, we separate the overlapping diffraction signals by analyzing individual pixel counts and applying pattern recognition. The helium nanodroplets’ spherical shape allows us to cross-validate this approach by fitting the radial scattering profiles with Mie solutions for abichromatic field. The excellent agreement between the two methods, particularly in the sparsely illuminated outer regions of the diffraction patterns where high-resolution structural information is encoded, highlights the quality of this approach and its potential for future advanced X-ray movie techniques. Despite recent advances in X-ray imaging, resolving ultrafast X-ray-induced structural dynamics in individual nanoparticles remains challenging. Here, the authors advance two-color X-ray imaging schemes with XFELs to probe those dynamics in helium nanodroplets by introducing a new computational image-separation method.

Single-shot coherent diffractive imaging with intense short-wavelength light pulses enables the structural characterization of individual nanoparticles in free flight with high spatial and temporal resolution. Conventional coherent diffractive imaging assumes that the target object exhibits a linear scattering response and static electronic properties. Here, we extend this approach to investigating transient-laser-driven modifications of the electronic structure in individual nanoparticles, imprinted in their time-resolved diffraction patterns. In the presence of a near-infrared laser pulse, we observe a pronounced reduction in the diffraction signal from helium nanodroplets when probed with ultrashort extreme ultraviolet pulses. This effect is attributed to a light-field-induced modification of the electronic structure of the droplets, which substantially increases their extreme ultraviolet absorption. Our results demonstrate the possibility to capture ultrafast light-driven electron dynamics in nanoscale systems with single-particle diffraction. This opens a pathway toward the spatiotemporal tracking of reversible changes in the electronic properties of nanoscale structures with potential applications in ultrafast x-ray optics, materials science, and all-optical signal processing.

X-ray free-electron lasers can nowadays deliver pairs of ultrabright, ultrashort light pulses with controllable delays at different photon energies. When combined with diffraction experiments, the interaction of these pulses with a sample at different times can produce two snapshots of an evolving system, enabling spatial and temporal resolution of ultrafast dynamics in nanomatter at and beyond the terahertz time scale. However, light detectors are orders of magnitude slower. The diffraction signals from the two pulses overlap in the recorded data and cannot be separated using currently available analysis methods. Here, we address this challenge by introducing Dichography, a diffraction imaging technique that restores the two unique views of the sample from superimposed scattering signals. We apply Dichography to experimental diffraction patterns of isolated xenon-doped superfluid helium nanodroplets, imaged using time-delayed, two-color X-ray pulses at intensities near the detection limit. The reconstructed images provide evidence of the survival of the xenon structures up to 750 fs after the interaction with the first shot. The capabilities of Dichography are further explored by applying the method to data from a second experiment, in which we retrieve the images of two distinct silver nanoparticles intercepted by the same light pulse. Dichography enables a new class of experiments for spatially and temporally resolving ultrafast phenomena, making a significant step toward the original promise of X-ray free-electron lasers to capture ultrafast movies of nanomatter.

The advent of isolated and intense sub-femtosecond X-ray pulses enables tracking of quantummechanical motion of electrons in molecules and solids. The combination of X-ray spectroscopy and diffraction imaging is a powerful approach to visualize non-equilibrium dynamics in systems beyond few atoms. However, extreme x-ray intensities introduce significant electronic damage, limiting material contrast and spatial resolution. Here we show that newly available intense subfemtosecond (sub-fs) x-ray FEL pulses can outrun most ionization cascades and partially reverse x-ray damage through stimulated x-ray emission in the vicinity of a resonance. In our experiment, we compared thousands of coherent x-ray diffraction patterns and simultaneously recorded ion spectra from individual Ne nanoparticles injected into the FEL focus. Our experimental results and theoretical modeling reveal that x-ray diffraction increases and the average charge state decreases in particles exposed to sub-fs pulses compared to those illuminated with 15-femtosecond pulses. Sub-fs exposures outrun most Auger decays and impact ionization processes, and enhance nonlinear effects such as stimulated emission, which cycle bound electrons between different states. These findings demonstrate that intense sub-fs x-ray FEL pulses are transformative for advancing high-resolution imaging and spectroscopy in chemical and material sciences, and open the possibilities of coherent control of the interaction between x-rays and complex specimen beyond few atoms.

We report on time-resolved coherent diffraction imaging of gas-phase silver nanoparticles, strongly heated via their plasmon resonance. The x-ray diffraction images reveal a broad range of phenomena for different excitation strengths, from simple melting over strong cavitation to explosive disintegration. Molecular dynamics simulations fully reproduce this behavior and show that the heating induces rather similar trajectories through the phase diagram in all cases, with the very different outcomes resulting solely from whether and where the stability limit of the metastable superheated liquid is crossed.

Coherent Diffraction Imaging (CDI) is an experimental technique to image isolated structures by recording the scattered light. The sample density can be recovered from the scattered field through a Fourier Transform operation. However, the phase of the field is lost during the measurement and has to be algorithmically retrieved. Here we present SPRING, an analysis framework tailored to X-ray Free Electron Laser (XFEL) single-shot single-particle diffraction data that implements the Memetic Phase Retrieval method to mitigate the shortcomings of conventional algorithms. We benchmark the approach on data acquired in two experimental campaigns at SwissFEL and European XFEL. Results reveal unprecedented stability and resilience of the algorithm’s behavior on the input parameters, and the capability of identifying the solution in conditions hardly treatable with conventional methods. A user-friendly implementation of SPRING is released as open-source software, aiming at being a reference tool for the CDI community at XFEL and synchrotron facilities.

Because of their high photon flux, x-ray free-electron lasers (FEL) allow to resolve the structure of individual nanoparticles via coherent diffractive imaging (CDI) within a single x-ray pulse. Since the inevitable rapid destruction of the sample limits the achievable resolution, a thorough understanding of the spatiotemporal evolution of matter on the nanoscale following the irradiation is crucial. We present a technique to track x-ray induced structural changes in time and space by recording two consecutive diffraction patterns of the same single, free-flying nanoparticle, acquired separately on two large-area detectors opposite to each other, thus examining both the initial and evolved particle structure. We demonstrate the method at the extreme ultraviolet (XUV) and soft x-ray Free-electron LASer in Hamburg (FLASH), investigating xenon clusters as model systems. By splitting a single XUV pulse, two diffraction patterns from the same particle can be obtained. For focus intensities of about 2x1012 W cm-2 we observe still largely intact clusters even at the longest delays of up to 650 picoseconds of the second pulse, indicating that in the highly absorbing systems the damage remains confined to one side of the cluster. Instead, in case of five times higher flux, the diffraction patterns show clear signatures of disintegration, namely increased diameters and density fluctuations in the fragmenting clusters. Future improvements to the accessible range of dynamics and time resolution of the approach are discussed.

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.

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.

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 excitation of atomic clusters and nanodroplets in strong laser fields is an ideal model scenario for studying the ultrafast physical processes underlying the formation and evolution of highly excited matter. Particularly insightful experiments with high temporal and spatial resolution have recently become possible: Via single-particle coherent diffractive imaging (CDI) using the intense femtosecond pulses of X-ray free-electron lasers (X-FELs), a single, isolated cluster can be “snapshot”-imaged in free flight and in parallel, the residuals of this single event (e.g. ions, electrons, fluorescence) can be captured, instead of the usual averaging over ensembles of clusters [1].

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 even encode three-dimensional morphological information of the samples, but the retrieval of this information remains a challenge. Up to now, effective three-dimensional morphology reconstructions from single shots were only achieved via fitting with highly constrained models, requiring a priori knowledge about possible geometrical shapes. 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 which were not accessible previously. Our results open new routes towards true 3D structure determination of single nanoparticles and, ultimately, 3D movies of ultrafast nanoscale dynamics.

X-ray and extreme ultraviolet (XUV) coherent diffractive imaging (CDI) have the advantage of producing high resolution images with current spatial resolution of tens of nanometers and temporal resolution of tens of femtoseconds. Modern developments in the production of coherent, ultra-bright, and ultra-short X-ray and XUV pulses have even enabled lensless, single-shot imaging of individual, transient, non-periodic objects. The data collected in this technique are diffraction images, which are intensity distributions of the scattered photons from the object. Superfluid helium droplets are ideal systems to study with CDI, since each droplet is unique on its own. It is also not immediately apparent what shapes the droplets would take or what structures are formed by dopant particles inside the droplet. In this chapter, we review the current state of research on helium droplets using CDI, particularly, the study of droplet shape deformation, the in-situ configurations of dopant nanostructures, and their dynamics after being excited by an intense laser pulse. Since CDI is a rather new technique for helium nanodroplet research, we also give a short introduction on this method and on the different light sources available for X-ray and XUV experiments.

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.

We have explored the light induced dynamics in superfluid helium nanodroplets with wide-angle scattering in a pump-probe measurement scheme. The droplets are doped with xenon atoms to facilitate the ignition of a nanoplasma through irradiation with near-infrared laser pulses. After a variable time delay of up to 800 ps, we image the subsequent dynamics using intense extreme ultraviolet pulses from the FERMI free-electron laser. The recorded scattering images exhibit complex intensity fluctuations that are categorized based on their characteristic features. Systematic simulations of wide-angle diffraction patterns are performed, which can qualitatively explain the observed features by employing model shapes with both randomly distributed as well as structured, symmetric distortions. This points to a connection between the dynamics and the positions of the dopants in the droplets. In particular, the structured fluctuations might be governed by an underlying array of quantized vortices in the superfluid droplet as has been observed in previous small-angle diffraction experiments. Our results provide a basis for further investigations of dopant-droplet interactions and associated heating mechanisms.

Interatomic processes play a crucial role in weakly bound complexes exposed to ionizing radiation; therefore, gaining a thorough understanding of their efficiency is of fundamental importance. Here, we directly measure the timescale of interatomic Coulombic decay (ICD) in resonantly excited helium nanodroplets using a high-resolution, tunable, extreme ultraviolet free-electron laser. Over an extensive range of droplet sizes and laser intensities, we discover the decay to be surprisingly fast, with decay times as short as 400 fs, nearly independent of the density of the excited states. Using a combination of time-dependent density functional theory and ab initio quantum chemistry calculations, we elucidate the mechanisms of this ultrafast decay process, where pairs of excited helium atoms in one droplet strongly attract each other and form merging void bubbles, which drastically accelerates ICD.

Bruno Langbehn∗1, Yevheniy Ovcharenko∗,†, Daniela Rupp∗, Katharina Sander‡, Christian Peltz‡, Andrew Clark§, Marcello Coreno¶, Riccardo Cucini¶, Paola Finetti¶, Michele Di Fraia¶, Cesare Grazioli¶, Denys Iablonskyi∗∗, Aaron C. LaForge††, Verónica Oliver Álvarez de Lara§, Oksana Plekan¶, Paolo Piseri‡‡, Toshiyuki Nishiyama§§, Carlo Callegari¶, Kevin C. Prince¶,¶¶, Kyoshi Ueda∗∗, Frank Stienkemeier††, Thomas Fennel∗∗∗,‡, and Thomas Möller∗

When weakly-bound complexes are multiply excited by intense electromagnetic radiation, energy can be exchanged between neighboring atoms through a type of resonant interatomic Coulombic decay (ICD). This decay mechanism due to multiple excitations has been predicted to be relatively slow, typically lasting tens to hundreds of picoseconds. Here, we directly measure the ICD timescale in resonantly excited helium droplets using a high resolution, tunable, extreme ultraviolet free electron laser. Over an extensive range of droplet sizes and laser intensities, we discover the decay to be surprisingly fast, with decay times as fast as 400 femtoseconds, and to only present a weak dependence on the density of the excited states. Using a combination of time dependent density functional theory and ab initio quantum chemistry calculations, we elucidate the mechanisms of this ultrafast decay process where pairs of excited helium atoms in one droplet strongly attract each other and form merging void bubbles which drastically accelerates ICD.