We measure molecular vibrations with femtometer precision using time-resolved x-ray absorption spectroscopy. For a demonstration, a Raman process excites the A$_{1g}$ mode in gas-phase SF$_6$ molecules with an amplitude of $\approx50$ fm, which is probed by a time-delayed soft x-ray pulse at the sulfur $L_{2,3}$-edge. Mapping the extremely small measured energy shifts to internuclear distances requires an understanding of the electronic contributions provided by a many-body ab initio simulation. Our study establishes core-level spectroscopy as a precision tool for time-dependent molecular-structure metrology.

The electronic and nuclear dynamics inside molecules are essential for chemical reactions, where different pathways typically unfold on ultrafast timescales. Extreme ultraviolet (XUV) light pulses generated by free-electron lasers (FELs) allow atomic-site and electronic-state selectivity, triggering specific molecular dynamics while providing femtosecond resolution. Yet, time-resolved experiments are either blind to neutral fragments or limited by the spectral bandwidth of FEL pulses. Here, we combine a broadband XUV probe pulse from high-order harmonic generation with an FEL pump pulse to observe dissociation pathways leading to fragments in different quantum states. We temporally resolve the dissociation of a specific O2+ state into two competing channels by measuring the resonances of ionic and neutral fragments. This scheme can be applied to investigate convoluted dynamics in larger molecules relevant to diverse science fields.

We report the measurement of the photoelectron angular distribution of two-photon single-ionization near the 2p^{2} ^{1}D^{e} double-excitation resonance in helium, benchmarking the fundamental nonlinear interaction of two photons with two correlated electrons. This observation is enabled by the unique combination of intense extreme ultraviolet pulses, delivered at the high-repetition-rate free-electron laser in Hamburg (FLASH), ionizing a jet of cryogenically cooled helium atoms in a reaction microscope. The spectral structure of the intense self-amplified spontaneous emission free-electron laser pulses has been resolved on a single-shot level to allow for post selection of pulses, leading to an enhanced spectral resolution, and introducing a new experimental method. The measured angular distribution is directly compared to state-of-the-art theory based on multichannel quantum defect theory and the streamlined R-matrix method. These results and experimental methodology open a promising route for exploring fundamental interactions of few photons with few electrons in general.

We study the interaction of intense extreme ultraviolet (XUV) light with the 2s2p doubly excited state in helium. In addition to previously understood energy-level and phase shifts, high XUV intensities may lead to other absorption-line-shape distortions. Here, we report on experimental transient-absorption spectroscopy results on the 2s2p line-width modification in helium in intense stochastic XUV fields. A few-level-model simulation is realized to investigate the origins of this effect. We find that the line-shape broadening is connected to the strong coupling of the ground state to the 2s2p doubly excited state which is embedded in the ionization continuum. As the broadening takes place for intensities lower than for other strong-coupling processes, e.g. observed asymmetry changes of the absorption profile, this signature can be identified already in an intermediate intensity regime. These findings are in general relevant for resonant inner-shell transitions in nonlinear experiments with XUV and x-ray photon energies at high intensity.

We measure the perturbatively excited symmetric breathing mode vibration A 1 g in SF 6 via time-resolved x-ray absorption spectroscopy. Vibrational amplitudes of 50 fm were resolved. An ab-initio simulation confirms the results and reveals additional electronic coupling.

Electronic interactions play a fundamental role in atoms, molecular structure and reactivity. We introduce a general concept to control the effective electronic exchange interaction with intense laser fields via coupling to excited states. As an experimental proof of principle, we study the SF_{6} molecule using a combination of soft x-ray and infrared (IR) laser pulses. Increasing the IR intensity increases the effective exchange energy of the core hole with the excited electron by 50%, as observed by a characteristic spin-orbit branching ratio change. This work demonstrates altering electronic interactions by targeting many-particle quantum properties.

In this work, we use an extreme-ultraviolet (XUV) free-electron laser (FEL) to resonantly excite the I:4d(5/2)(-sigma*) transition of a gas-phase di-iodomethane (CH2I2) target. This site-specific excitation generates a 4d core hole located at an iodine site, which leaves the molecule in a well-defined excited state. We subsequently measure the time-dependent absorption change of the molecule with the FEL probe spectrum centered on the same I: 4d resonance. Using ab initio calculations of absorption spectra of a transient isomerization pathway observed in earlier studies, our time-resolved measurements allow us to assign the timescales of the previously reported direct and indirect dissociation pathways. The presented method is thus sensitive to excited-state molecular geometries in a time-resolved manner, following a core-resonant site-specific trigger.

Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s1. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures2,3. Here we study this possibility in an antiferromagnetic axion insulator-even-layered, two-dimensional MnBi2Te4-in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect-the layer Hall effect-in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi2Te4 shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e2/h (where e is the electron charge and h is Planck's constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets4-9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

Precision magnetometry is fundamental to the development of novel magnetic materials and devices. Recently, the nitrogen-vacancy (NV) center in diamond has emerged as a promising probe for static magnetism in 2D van der Waals materials, capable of quantitative imaging with nanoscale spatial resolution. However, the dynamic character of magnetism, crucial for understanding the magnetic phase transition and achieving technological applications, has rarely been experimentally accessible in single 2D crystals. Here, we coherently control the NV center's spin precession to achieve ultra-sensitive, quantitative ac susceptometry of a 2D ferromagnet. Combining dc hysteresis with ac susceptibility measurements varying temperature, field, and frequency, we illuminate the formation, mobility, and consolidation of magnetic domain walls in few-layer CrBr3. We show that domain wall mobility is enhanced in ultrathin CrBr3, with minimal decrease for excitation frequencies exceeding hundreds of kilohertz, and is influenced by the domain morphology and local pinning of the flake. Our technique extends NV magnetometry to the multi-functional ac and dc magnetic characterization of wide-ranging spintronic materials at the nanoscale.

We performed a time-resolved spectroscopy experiment on the dissociation of oxygen molecules after the interaction with intense extreme-ultraviolet (XUV) light from the free-electron laser in Hamburg at Deutsches Elektronen-Synchrotron. Using an XUV-pump/XUV-probe transient-absorption geometry with a split-and-delay unit, we observe the onset of electronic transitions in the O2+ cation near 50 eV photon energy, marking the end of the progression from a molecule to two isolated atoms. We observe two different time scales of 290 ± 53 and 180 ± 76 fs for the emergence of different ionic transitions, indicating different dissociation pathways taken by the departing oxygen atoms. With regard to the emerging opportunities of tuning the central frequencies of pump and probe pulses and of increasing the probe–pulse bandwidth, future pump–probe transient-absorption experiments are expected to provide a detailed view of the coupled nuclear and electronic dynamics during molecular dissociation.

The emergence of ultra-intense extreme-ultraviolet (XUV) and X-ray free-electron lasers (FELs) has opened the door for the experimental realization of non-linear XUV and X-ray spectroscopy techniques. Here we demonstrate an experimental setup for an all-XUV transient absorption spectroscopy method for gas-phase targets at the FEL. The setup combines a high spectral resolving power of E/ΔE ≈ 1500 with sub-femtosecond interferometric resolution, and covers a broad XUV photon-energy range between approximately 20 and 110 eV. We demonstrate the feasibility of this setup firstly on a neon target. Here, we intensity- and time-resolve key aspects of non-linear XUV-FEL light-matter interactions, namely the non-resonant ionization dynamics and resonant coupling dynamics of bound states, including XUV-induced Stark shifts of energy levels. Secondly, we show that this setup is capable of tracking the XUV-initiated dissociation dynamics of small molecular targets (oxygen and diiodomethane) with site-specific resolution, by measuring the XUV transient absorption spectrum. In general, benefitting from a single-shot detection capability, we show that the setup and method provides single-shot phase-locked XUV pulse pairs. This lays the foundation to perform, in the future, experiments as a function of the XUV interferometric time delay and the relative phase, which enables advanced coherent non-linear spectroscopy schemes in the XUV and X-ray spectral range.

High-intensity ultrashort pulses at extreme ultraviolet (XUV) and x-ray photon energies, delivered by state-of-the-art free-electron lasers (FELs), are revolutionizing the field of ultrafast spectroscopy. For crossing the next frontiers of research, precise, reliable and practical photonic tools for the spectro-temporal characterization of the pulses are becoming steadily more important. Here, we experimentally demonstrate a technique for the direct measurement of the frequency chirp of extreme-ultraviolet free-electron laser pulses based on fundamental nonlinear optics. It is implemented in XUV-only pump-probe transient-absorption geometry and provides in-situ information on the time-energy structure of FEL pulses. Using a rate-equation model for the time-dependent absorbance changes of an ionized neon target, we show how the frequency chirp can be directly extracted and quantified from measured data. Since the method does not rely on an additional external field, we expect a widespread implementation at FELs benefiting multiple science fields by in-situ on-target measurement and optimization of FEL-pulse properties.

We report on experimental soft-x-ray transient absorption spectroscopy in SF 6 . The influences of strong SWIR fields and of vibrational dynamics initiated by impulsive stimulated Raman scattering on the 6 a 1 g S 2 p 1 / 2 , 3 / 2 − 1 resonance are investigated.

We present a technique for the direct measurement of the frequency chirp of high-frequency free-electron-laser pulses based on fundamental nonlinear optics. It is implemented in transient absorption geometry.

We report on soft x-ray transient absorption spectroscopy in SF6. The influences of strong SWIR fields and of impulsive stimulated Raman scattering initiated ν1 vi-brational breathing mode dynamics on the 6a1 g (S 2p1/2, 3 / 2) - 1 resonance are investigated.

We report on numerical results revealing line-shape asymmetry changes of electronic transitions in atoms near-resonantly driven by intense extreme-ultraviolet (XUV) electric fields by monitoring their transient absorption spectrum after transmission through a moderately dense atomic medium. Our numerical model utilizes ultrashort broadband XUV laser pulses varied in their intensity (1014–1015 W/cm2) and detuning nearly out of resonance for a quantitative evaluation of the absorption line-shape asymmetry. It will be shown how transient energy shifts of the bound electronic states can be linked to these asymmetry changes in the case of an ultrashort XUV driving pulse temporally shorter than the lifetime of the resonant excitation, and how the asymmetry can be controlled by the near-resonant detuning of the XUV pulse. In the case of a two-level system, the numerical model is compared to an analytical calculation, which helps to uncover the underlying mechanism for the detuning- and intensity-induced line-shape modification and links it to the generalized Rabi frequency. To further apply the numerical model to recent experimental results of the near-resonant dressing of the 2s2p doubly excited state in helium by an ultrashort XUV free-electron laser pulse we extend the two-level model with an ionization continuum, thereby enabling the description of transmission-type (Fraunhofer-like) transient absorption of a strongly laser-coupled autoionizing state.

Two-electron dynamics of an excited model atom interacting with moderately strong laser fields is analyzed in the time domain. We solve the time-dependent Schrodinger equation (TDSE) for two electrons confined to the same one-dimensional configuration space, accounting also for the electron-electron interaction. The computational method allows direct access to the time-dependent population of the relevant atomic states during and right after the interaction with a near-infrared (NIR) laser pulse. We compare the ionization dynamics of singly excited states and doubly excited states. We find that doubly-excited initial states exhibit enhanced double ionization yield, with non-trivial dynamics including contributions from direct and sequential processes, while the electrons leave the atom either back-to-back or in the same direction.

We demonstrate time-resolved nonlinear extreme-ultraviolet absorption spectroscopy on multiply charged ions, here applied to the doubly charged neon ion, driven by a phase-locked sequence of two intense free-electron laser pulses. Absorption signatures of resonance lines due to 2p-3d bound-bound transitions between the spin-orbit multiplets ^{3}P_{0,1,2} and ^{3}D_{1,2,3} of the transiently produced doubly charged Ne^{2+} ion are revealed, with time-dependent spectral changes over a time-delay range of (2.4±0.3)  fs. Furthermore, we observe 10-meV-scale spectral shifts of these resonances owing to the ac Stark effect. We use a time-dependent quantum model to explain the observations by an enhanced coupling of the ionic quantum states with the partially coherent free-electron laser radiation when the phase-locked pump and probe pulses precisely overlap in time.

We report on the experimental observation of a strong-field dressing of an autoionizing two-electron state in helium with intense extreme-ultraviolet laser pulses from a free-electron laser. The asymmetric Fano line shape of this transition is spectrally resolved, and we observe modifications of the resonance asymmetry structure for increasing free-electron-laser pulse energy on the order of few tens of Microjoules. A quantum-mechanical calculation of the time-dependent dipole response of this autoionizing state, driven by classical extreme-ultraviolet (XUV) electric fields, evidences strong-field-induced energy and phase shifts of the doubly excited state, which are extracted from the Fano line-shape asymmetry. The experimental results obtained at the Free-Electron Laser in Hamburg (FLASH) thus correspond to transient energy shifts on the order of a few meV, induced by strong XUV fields. These results open up a new way of performing nonperturbative XUV nonlinear optics for the light-matter interaction of resonant electronic transitions in atoms at short wavelengths.