Andrei Benediktovitch

Irradiation of solids with focused femtosecond XFEL pulses can drive them into warm dense matter (WDM) and populate excited electronic configurations that enable otherwise Pauli-blocked bound-bound transitions. These transient resonances substantially increase x-ray opacity and the elastic scattering factor. Here, we observe a transient enhancement of Cu elastic scattering near the L3 edge via Lα (2p–3d) transitions at 929.7 eV. The excitation sequence starts with photoionization, followed by Auger decay that produces high-energy electrons. These then trigger electron-impact ionization, creating a non-local thermodynamic (non-LTE) state. On a fs timescale, Cu ions remain at their cold-solid equilibrium positions while occupying excited electronic configurations with multiple 3d holes. Using XFEL pulses elastically scattered from a Cu-containing [SiC/Cu/B4C] multilayer, we spectrally resolve a multilayer-superlattice Bragg peak around the Lα resonance. Its amplitude and spectral width increase nonlinearly with excitation intensity. A self-consistent theory describing the formation of the non-LTE state and its x-ray optical properties links transient electronic configurations to the measured scattering response and reproduces the data. An effective two-level model quantifies a twelvefold enhancement of the imaginary scattering factor relative to cold Cu, demonstrating the role of transient resonances and enabling ionization- and state-selective contrast for ultrafast x-ray imaging.

Recent progress in ultrafast x-ray sources helped establish x-rays as an important tool for probing lattice and magnetic dynamics initiated by femtosecond optical pulses. Here, we explore the potential of ultrashort hard x-ray pulses for driving magnetic dynamics. We use a transient grating technique in which a spatially periodic x-ray excitation pattern gives rise to material excitations at a well-defined wave vector, whose dynamics are monitored via diffraction of an optical probe pulse. The excitation of a ferrimagnetic gadolinium bismuth iron garnet film placed in an external tilted magnetic field by x-rays at the Gd L_{3} edge results in both magnetic and nonmagnetic transient gratings whose contributions to the diffracted signal are separated by polarization analysis. We observe the magnetization precession at both longitudinal acoustic and spin wave frequencies. An analysis with the Landau-Lifshitz-Gilbert equation indicates that the magnetization precession is driven by strain resulting from thermal expansion induced by absorbed x-rays. The results establish x-ray transient gratings as a tool for driving coherent phonons and magnons, with the potential of accessing wave vectors across the entire Brillouin zone.

Since the invention of the laser, nonlinear effects such as filamentation¹, Rabi cycling^2,3 and collective emission⁴ have been explored in the optical regime, leading to a wide range of scientific and industrial applications^5,6,7,8. X-ray free-electron lasers (XFELs) have extended many optical techniques to X-rays for their advantages of ångström-scale spatial resolution and elemental specificity⁹. An example is XFEL-driven inner-shell Kα₁ (2p_3/2 → 1s_1/2) X-ray lasing in elements ranging from neon to copper, which has been used for nonlinear spectroscopy and development of new X-ray laser sources^{10,11,12,13,14,15,16}. Here we show that strong lasing effects similar to those in the optical regime can occur at 1.5–2.1 Å wavelengths during high-intensity (>10¹⁹ W cm⁻²) XFEL-driven Kα₁ lasing of copper and manganese. Depending on the temporal XFEL pump pulse substructure, the resulting X-ray pulses (about 10⁶−10⁸ photons) can exhibit strong spatial inhomogeneities and spectral splitting, inhomogeneities and broadening. Three-dimensional Maxwell–Bloch calculations¹⁷ show that the observed spatial inhomogeneities result from X-ray filamentation and that the broad spectral features are driven by sub-femtosecond Rabi cycling. Our simulations indicate that these X-ray pulses can have pulse lengths of less than 100 attoseconds and coherence properties that provide opportunities for quantum X-ray optics applications.

Quantum field theory predicts a nonlinear response of the vacuum to strong electromagnetic fields of macroscopic extent. This fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory. A particularly distinct signature of the resulting optical activity of the quantum vacuum is vacuum birefringence. This offers an excellent opportunity for a precision test of nonlinear quantum electrodynamics in an uncharted parameter regime. Recently, the operation of the high-intensity Relativistic Laser at the X-ray Free Electron Laser provided by the Helmholtz International Beamline for Extreme Fields has been inaugurated at the High Energy Density scientific instrument of the European X-ray Free Electron Laser. We make the case that this worldwide unique combination of an X-ray free-electron laser and an ultra-intense near-infrared laser together with recent advances in high-precision X-ray polarimetry, refinements of prospective discovery scenarios and progress in their accurate theoretical modelling have set the stage for performing an actual discovery experiment of quantum vacuum nonlinearity.

Warm dense matter is at the boundary between a plasma and a condensed phase and plays a role in astrophysics, planetary science and inertial confinement fusion research. However, its electronic structure and ionic structure upon irradiation with strong laser pulses remain poorly understood. Here, we use an intense and ultrafast X-ray free-electron laser pulse to simultaneously create and characterize warm dense copper using L-edge X-ray absorption spectroscopy over a large irradiation intensity range. Below a pulse intensity of 10¹⁵ W cm⁻², an absorption peak below the L edge appears, originating from transient depletion of the 3d band. This peak shifts to lower energy with increasing intensity, indicating the movement of the 3d band upon strong X-ray excitation. At higher intensities, substantial ionization and collisions lead to the transition from reverse saturable absorption to saturable absorption of the X-ray free-electron laser pulse, two nonlinear effects that hold promise for X-ray pulse-shaping. We employ theoretical calculations that combine a model based on kinetic Boltzmann equations with finite-temperature real-space density-functional theory to interpret these observations. The results can be used to benchmark non-equilibrium models of electronic structure in warm dense matter.

An approach to modeling the dynamics of x-ray amplified spontaneous emission and superfluorescence, the phenomenon of collective x-ray emission initiated by intense pulses of x-ray free-electron lasers, is developed based on stochastic partial differential equations. The equations are derived from first principles, and the relevant approximations, derivation steps, and extensions specific to stimulated x-ray emission are presented. The resulting equations take the form of three-dimensional generalized Maxwell-Bloch equations augmented with noise terms for both field and atomic variables. The derived noise terms possess specific correlation properties that enable the correct reconstruction of spontaneous emission. Consequently, the developed theoretical formalism is universally suitable for describing all stages of stimulated x-ray emission: spontaneous emission, amplified spontaneous emission, and superfluorescence. We present numerical examples that illustrate various properties of the emitted field, including spatiotemporal coherence and spectral-angular and polarization characteristics. We anticipate that the proposed theoretical framework will establish a robust foundation for interpreting measurements in stimulated x-ray emission spectroscopy, modeling x-ray laser oscillators, and describing other experiments leveraging x-ray superfluorescence.

Intense focused XFEL pulses can produce atoms in the core-hole state thus leading to collective x-ray emission (superfluorescence). We will present a 3 D description of paraxial x-ray superfluorescence based on rigorously derived stochastic differential equations.

Fisher information is a powerful mathematical tool suitable for quantification of data `informativity' and optimization of the experimental setup and measurement conditions. Here, it is applied to X-ray diffraction and an informational approach to choosing the optimal measurement configuration is proposed. The core idea is maximization of the information which can be extracted from the measured data set by the selected analysis technique, over the sets of accessible reflections and measurement geometries. The developed approach is applied to high-resolution X-ray diffraction measurements and microstructure analysis of multilayer samples, and its efficiency and consistency are demonstrated with the results of more straightforward Monte Carlo simulations.

Amplified spontaneous XUV emission from Xenon clusters irradiated by free-electron laser pulses was experimentally observed. Theoretical modeling describes experi-mental trends and shows that collision processes in expanding clusters yield transient pop-ulation inversion and cause decoherence.