Femtosecond electronic response of atoms to ultra-intense X-rays

The dynamics of plasmon-induced hot carrier creation in colloidal gold

The generation and dynamics of plasmon-induced hot carriers in gold nanoparticles offer crucial insights into nonequilibrium states for energy applications, yet the underlying mechanisms remain experimentally elusive. Here, we leverage ultrafast X-ray absorption spectroscopy (XAS) to directly capture hot carrier dynamics with sub-50 fs temporal resolution, providing clear evidence of plasmon decay mechanisms. We observe the sequential processes of Landau damping (~25 fs) and hot carrier thermalization (~1.5 ps), identifying hot carrier formation as a significant decay pathway. Energy distribution measurements reveal carriers in non-Fermi-Dirac states persisting beyond 500 fs and observe electron populations exceeding single-photon excitation energy, indicating the role of an Auger heating mechanism alongside traditional impact excitation. These findings deepen the understanding of hot carrier behavior under localized surface plasmon resonance, offering valuable implications for applications in photocatalysis, photovoltaics, and phototherapy. This work establishes a methodological framework for studying hot carrier dynamics, opening avenues for optimizing energy transfer processes in nanoscale plasmonic systems.

Probing soft X-ray induced photoreduction of a model Mn-complex at cryogenic conditions

Soft X-ray absorption spectroscopy of first row transition elements at their respective L-edges provides important information about the oxidation and spin states of the metal centers. However, the associated sample damage in radiation-sensitive samples substantially alters the electronic and chemical structures of redox-active metal centers. Here, we measure the soft X-ray spectrum of the model MnIII(acac)3 complex containing a redox-active MnIII metal center in an octahedral environment with a superconducting transition-edge sensor detector. To reduce the secondary damage resulting primarily from the diffusion of radicals and electrons, the spectra are collected at 30 K and 80 K on solid samples. Starting from the first scan, we detect the contribution of X-ray induced sample damage leading to a change in the MnII intensity. However, at low temperatures, particularly at 30 K, we do not observe a gradual increase in the radiation damage with successive scans with the X-ray beam at the same spot. At our estimated dose of 90 kGy, we find 62% of MnIII(acac)3 is still intact at 30 K. However, at room temperature, we see a gradual increase in radiation damage with increasing numbers of scans at the same spot, which is consistent with the possibility of increased diffusion rates of secondary radicals and electrons as noted in other studies.

A versatile and transportable endstation for controlled molecule experiments

We report on a new versatile transportable endstation for controlled molecule (eCOMO) experiments providing a combination of molecular beam purification by electrostatic deflection and simultaneous ion and electron detection using velocity-map imaging (VMI). The b-type electrostatic deflector provides spatial dispersion of species based on their effective-dipole-moment-to-mass ratio. This enables selective investigation of molecular rotational quantum states, conformers, and molecular clusters. Furthermore, the double-sided VMI spectrometer equipped with two high-temporal-resolution event-driven Timepix3 cameras provides detection of all generated ions independently of their mass-over-charge ratio and electrons. To demonstrate the potential of this novel apparatus, we present experimental results from our investigation of carbonyl sulfide (OCS) after ionization. In particular, we provide the characterization of the molecular beam, electrostatic deflector, and electron- and ion-VMI spectrometer. The eCOMO endstation delivers a platform for ultrafast dynamics studies using a wide range of light sources from table-top lasers to free-electron-laser and synchrotron-radiation facilities. This makes it suitable for research activities spanning from atomic, molecular, and cluster physics, over energy science and chemistry, to structural biology.

Non-linear enhancement of ultrafast X-ray diffraction through transient resonances

Diffraction-before-destruction imaging with ultrashort X-ray pulses can visualize non-equilibrium processes, such as chemical reactions, with sub-femtosecond precision in the native environment. Here, a nanospecimen diffracts a single X-ray flash before it disintegrates. The sample structure can be reconstructed from the coherent diffraction image (CDI). State-of-the-art X-ray snapshots lack high spatial resolution because of weak diffraction signal. Bleaching effects from photo-ionization significantly restrain image brightness scaling. We find that non-linear transient ion resonances can overcome this barrier if X-ray laser pulses are shorter than in most experiments. We compared snapshots from individual  ≈ 100 nm Xe nanoparticles as a function of pulse duration and incoming X-ray fluence. Our experimental results and Monte Carlo simulations suggest that transient resonances can increase ionic scattering cross sections significantly beyond literature values. This provides a novel avenue towards substantial improvement of the spatial resolution in CDI in combination with sub-femtosecond temporal precision at the nanoscale.

Theoretical studies on M-shell relocalization of K-hole Mg ions produced by x-ray free-electron laser

In hot dense plasmas, orbital delocalization and relocalization considerably influence the ionization balance, equation of state and radiative properties of matter. A self-consistent plasma screening potential is applied in atomic structure calculations for solid-density Mg plasmas, generated by an x-ray free electron laser (XFEL). As the charge state increases, the M-shell orbitals of K-hole Mg ions gradually relocalize, beginning with Mg^{6+} at solid density. The level population distributions are determined by solving a time-dependent rate equation using fine-structure level accounting approximations. The predicted K_{α} emission spectra align well with XFEL experiments only when orbital relocalization is carefully accounted for, revealing that the 3d orbital of Mg^{7+} is delocalized, consistent with density functional theory calculations.

Strong-field quantum control in the extreme ultraviolet domain using pulse shaping

Tailored light-matter interactions in the strong coupling regime enable the manipulation and control of quantum systems with up to unit efficiency1,2, with applications ranging from quantum information to photochemistry3-7. Although strong light-matter interactions are readily induced at the valence electron level using long-wavelength radiation8, comparable phenomena have been only recently observed with short wavelengths, accessing highly excited multi-electron and inner-shell electron states9,10. However, the quantum control of strong-field processes at short wavelengths has not been possible, so far, because of the lack of pulse-shaping technologies in the extreme ultraviolet (XUV) and X-ray domain. Here, exploiting pulse shaping of the seeded free-electron laser (FEL) FERMI, we demonstrate the strong-field quantum control of ultrafast Rabi dynamics in helium atoms with high fidelity. Our approach reveals a strong dressing of the ionization continuum, otherwise elusive to experimental observables. The latter is exploited to achieve control of the total ionization rate, with prospective applications in many XUV and soft X-ray experiments. Leveraging recent advances in intense few-femtosecond to attosecond XUV to soft X-ray light sources, our results open an avenue to the efficient manipulation and selective control of core electron processes and electron correlation phenomena in real time.

Stimulated X-ray emission spectroscopy

We describe an emerging hard X-ray spectroscopy technique, stimulated X-ray emission spectroscopy (S-XES). S-XES has the potential to characterize the electronic structure of 3d transition metal complexes with spectral information currently not reachable and might lead to the development of new ultrafast X-ray sources with properties beyond the state of the art. S-XES has become possible with the emergence of X-ray free-electron lasers (XFELs) that provide intense femtosecond X-ray pulses that can be employed to generate a population inversion of core-hole excited states resulting in stimulated X-ray emission. We describe the instrumentation, the various types of S-XES, the potential applications, the experimental challenges, and the feasibility of applying S-XES to characterize dilute systems, including the Mn4Ca cluster in the oxygen evolving complex of photosystem II.

Coulomb Explosion Imaging of Complex Molecules Using Highly Charged Ions

Rapidly stripping off multiple electrons from the target and triggering complete fragmentation with each constituent atom being charged up are ideal prerequisites for Coulomb explosion imaging. Here, we demonstrate that highly charged ion beam with energy in the Bragg peak region is a powerful tool capable of meeting these requirements. Using the 112.5  keV/u C^{5+} beam, we successfully imaged the structures of pyridazine, pyrimidine, and pyrazine, three isomers of C_{4}H_{4}N_{2}, by detecting ionic fragments H^{+}, C^{2+}, C^{+}, and N^{+} in quadruple coincidence. The three isomers are unambiguously distinguished in the spectra of angular correlation between different fragments, and their structures are clearly visualized in momentum images. More importantly, taking the advantage of fast colliding interaction that creates high charge states on a subfemtosecond timescale, our approach effectively suppresses the distortion of molecular configuration during explosion, ensuring the high accuracy in structural imaging. This is confirmed by the quantitative agreement of momentum magnitudes between the point-charge model and the experiment for all fragments including hydrogen. Our work demonstrates that highly charged ion induced Coulomb explosion is a powerful tool for precisely imaging the initial structures of complex molecules.

Controlled molecule injector for cold, dense, and pure molecular beams at the European x-ray free-electron laser

A permanently available molecular-beam injection setup for controlled molecules (COMO) was installed and commissioned at the small quantum systems (SQS) instrument at the European x-ray free-electron laser (EuXFEL). A b-type electrostatic deflector allows for pure state-, size-, and isomer-selected samples of polar molecules and clusters. The source provides a rotationally cold (T ≈ 1 K) and dense (ρ ≈ 108 cm-3) molecular beam with pulse durations up to 100 µs generated by a new version of the Even-Lavie valve. Here, a performance overview of the COMO setup is presented along with characterization experiments performed both with an optical laser at the Center for Free-Electron-Laser Science and with x rays at EuXFEL under burst-mode operation. COMO was designed to be attached to different instruments at the EuXFEL, in particular, the SQS and single particles, clusters, and biomolecules (SPB) instruments. This advanced controlled-molecules injection setup enables x-ray free-electron laser studies using highly defined samples with soft and hard x-ray FEL radiation for applications ranging from atomic, molecular, and cluster physics to elementary processes in chemistry and biology.

Transmissions of an x-ray free electron laser pulse through Al: Influence of nonequilibrium electron kinetics

A theoretical model for investigating the radiative transfer of an x-ray free electron laser (XFEL) pulse is developed based on a one-dimensional radiative transfer equation. The population dynamics of energy levels is obtained by rate equation approximation coupling with the Fokker-Planck equation, in which the electron energy distribution function (EEDF) is self-consistently determined. As an illustrative example, XFEL pulse propagation through a solid-density aluminum (Al) is investigated. The characteristics of the temporal evolution of the x-ray pulse shape, level population, and EEDF are demonstrated. The EEDF usually has two parts in XFEL-Al interactions: the near equilibrium part in the lower energy regions and the nonequilibrium part in the higher energy region. The deep gap between the two parts is quickly filled in the solid-density Al plasma. The pulse shape is distorted and the duration shortens as the x-ray pulse propagates through the Al sample. The x-ray transmission spectra were compared with experimental and other theoretical results, and good agreement was found. There are slight discrepancies between the transmission obtained by solving the Fokker-Planck equation and Maxwellian assumptions because nonequilibrium electrons in the higher energy region account for only a small fraction of the total electrons.

Core Binding Energy Calculations: A Scalable Approach with the Quantum Embedding-Based Equation-of-Motion Coupled-Cluster Method

We investigated the use of density matrix embedding theory to facilitate the computation of core ionization energies (IPs) of large molecules at the equation-of-motion coupled-cluster singles doubles with perturbative triples (EOM-CCSD*) level in combination with the core-valence separation (CVS) approximation. The unembedded IP-CVS-EOM-CCSD* method with a triple-ζ basis set produced ionization energies within 1 eV of experiment with a standard deviation of ∼0.2 eV for the core65 data set. The embedded variant contributed very little systematic error relative to the unembedded method, with a mean unsigned error of 0.07 eV and a standard deviation of ∼0.1 eV, in exchange for accelerating the calculations by many orders of magnitude. By employing embedded EOM-CC methods, we computed the core ionization energies of the uracil hexamer, doped fullerene, and chlorophyll molecule, utilizing up to ∼4000 basis functions within 1 eV from experimental values. Such calculations are not currently possible with the unembedded EOM-CC method.

Numerical investigation of nonequilibrium electron effects on the collisional ionization rate in the collisional-radiative model

The interplay of kinetic electron physics and atomic processes in ultrashort laser-plasma interactions provides a comprehensive understanding of the impact of the electron energy distribution on plasma properties. Notably, nonequilibrium electrons play a vital role in collisional ionization, influencing ionization degrees and spectra. This paper introduces a computational model that integrates the physics of kinetic electrons and atomic processes, utilizing a Boltzmann equation for nonequilibrium electrons and a collisional-radiative model for atomic state populations. The model is used to investigate the influence of nonequilibrium electrons on collisional ionization rates and its effect on the population distribution, as observed in a widely known experiment [Young et al., Nature (London) 466, 56 (2010)0028-083610.1038/nature09177]. The study reveals a significant nonequilibrium electron presence during XFEL-matter interactions, profoundly affecting collisional ionization rates in the gas plasma, thereby necessitating careful consideration of the Collisional-Radiative model applied to such systems.

Transient responses of double core-holes generation in all-attosecond pump-probe spectroscopy

Double core-holes (DCHs) show remarkable and sensitive effects for understanding electron correlations and coherence. With advanced modulation of x-ray free-electron laser (XFEL) facility, we propose the forthcoming all-attosecond XFEL pump-probe spectroscopy can decipher the hidden photon-initiated dynamics of DCHs. The benchmark case of neon is investigated, and norm-nonconserving Monte-Carlo wavefunction method simulates non-Hermitian dynamics among vast states, which shows superiority in efficiency and reliability. In our scheme, population transfer to DCHs is sequentially irradiated by pump and probe laser. By varying time delay, Stark shifts and quantum path interference of resonant lines sensitively emerge at specific interval of two pulses. These ubiquitous multi-channel effects are also observed in phase-fluctuating pulses, derived from extra phases of impulsive Raman processes by pump laser. Non-perturbation absorption/emission verifies the uniquely interchangeable role of two pules in higher intensity. Our results reveal sensitive and robust responses on pulse parameters, which show potential capacity for XFEL attosecond pulse diagnosis and further attosecond-timescale chemical analysis.

Superradiant Thomson scattering from graphite in the extreme ultraviolet

We study the Thomson scattering from highly oriented pyrolitic graphite excited by the extreme ultraviolet, coherent pulses of FERMI free electron laser (FEL). An apparent nonlinear behavior is observed and fully described in terms of the coherent nature of both exciting FEL beam and scattered radiation, producing an intensity-dependent enhancement of the Thomson scattering cross-section. The process resembles Dicke's superradiant phenomenon and is thus interpreted as the observation of superradiant Thomson scattering. The process also triggers the creation of coherent, low-q ([Formula: see text] 0.3 Å[Formula: see text]), low energy phonons. The experimental data and analysis provide quantitative information on the sample characteristics, absorption, scattering factor, and coherent phonon energies and populations and open the route for the investigation of the deep nature of complex materials.

Millijoule Femtosecond X-Ray Pulses from an Efficient Fresh-Slice Multistage Free-Electron Laser

We present the generation of x-ray pulses with average pulse energies up to one millijoule and rms pulse durations down to the femtosecond level. We have produced these intense and short pulses by employing the fresh-slice multistage amplification scheme with a transversely tilted electron beam in a free-electron laser. In this scheme, a short pulse is produced in the first stage and later amplified by fresh parts of the electron bunch in up to a total of four stages of amplification. Our implementation is efficient, since practically the full electron beam contributes to produce the x-ray pulse. Our implementation is also compact, utilizing only 32 m of undulator. The demonstration was done at Athos, the soft x-ray beamline of SwissFEL, which was designed with high flexibility to take full advantage of the multistage amplification scheme. It opens the door for scientific opportunities following ultrafast dynamics using nonlinear x-ray spectroscopy techniques or avoiding electronic damage when capturing structures with a single intense pulse via single-particle imaging.

Alternative Pathway to Double-Core-Hole States

Excited double-core-hole states of isolated water molecules resulting from the sequential absorption of two x-ray photons have been investigated. These states are formed through an alternative pathway, where the initial step of core ionization is accompanied by the shake-up of a valence electron, leading to the same final states as in the core-ionization followed by core-excitation pathway. The capability of the x-ray free-electron laser to deliver very intense, very short, and tunable light pulses is fully exploited to identify the two different pathways.

Time-resolving state-specific molecular dissociation with XUV broadband absorption spectroscopy

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.

Multiple-core-hole resonance spectroscopy with ultraintense X-ray pulses

Understanding the interaction of intense, femtosecond X-ray pulses with heavy atoms is crucial for gaining insights into the structure and dynamics of matter. One key aspect of nonlinear light-matter interaction was, so far, not studied systematically at free-electron lasers-its dependence on the photon energy. Here, we use resonant ion spectroscopy to map out the transient electronic structures occurring during the complex charge-up pathways of xenon. Massively hollow atoms featuring up to six simultaneous core holes determine the spectra at specific photon energies and charge states. We also illustrate how different X-ray pulse parameters, which are usually intertwined, can be partially disentangled. The extraction of resonance spectra is facilitated by the possibility of working with a constant number of photons per X-ray pulse at all photon energies and the fact that the ion yields become independent of the peak fluence beyond a saturation point. Our study lays the groundwork for spectroscopic investigations of transient atomic species in exotic, multiple-core-hole states that have not been explored previously.

Simulations of collisional effects in an inner-shell solid-density Mg X-ray laser

Inner-shell [Formula: see text] X-ray lasers have been created by pumping gaseous, solid, and liquid targets with the intense X-ray output of free-electron lasers (FELs). For gaseous targets lasing relies on the creation of [Formula: see text]-shell core holes on a time-scale short compared with filling via Auger decay. In the case of solid and liquid density systems, collisional effects will also be important, affecting not only populations but also line-widths, both of which impact the degree of overall gain, and its duration. However, to date, such collisional effects have not been extensively studied. We present here initial simulations using the CCFLY code of inner-shell lasing in solid-density Mg, where we self-consistently treat the effects of the incoming FEL radiation and the atomic kinetics of the Mg system, including radiative, Auger and collisional effects. We find that the combination of collisional population of the lower states of the lasing transitions and broadening of the lines precludes lasing on all but the [Formula: see text] of the initially cold system. Even assuming instantaneous turning on of the FEL pump, we find the duration of the gain in the solid system to be sub-femtosecond. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Gain dynamics of inner-shell vacancy states pumped by high-intensity XFEL in Mg, Al and Si

High-intensity X-ray free-electron laser (XFEL) beams create transient and non-equilibrium dense states of matter in solid-density targets. These states can be used to develop atomic X-ray lasers with narrow bandwidth and excellent longitudinal coherence, which is not possible with current XFEL pulses. An atomic kinetics model is used to simulate the population dynamics of atomic inner-shell vacancy states in Mg, Al, and Si, revealing the feasibility of population inversion between K-shell and L-shell vacancy states. We also discuss the gain characteristics of these states implying the possibility of atomic X-ray lasers based on inner-shell vacancy states in the 1.5 keV region. The development of atomic X-ray lasers could have applications in high-resolution spectroscopy and nonlinear optics in the X-ray region.

Decreasing ultrafast x-ray pulse durations with saturable absorption and resonant transitions

Saturable absorption is a nonlinear effect where a material's ability to absorb light is frustrated due to a high influx of photons and the creation of electron vacancies. Experimentally induced saturable absorption in copper revealed a reduction in the temporal duration of transmitted x-ray laser pulses, but a detailed account of changes in opacity and emergence of resonances is still missing. In this computational work, we employ nonlocal thermodynamic equilibrium plasma simulations to study the interaction of femtosecond x rays and copper. Following the onset of frustrated absorption, we find that a K-M resonant transition occurring at highly charged states turns copper opaque again. The changes in absorption generate a transient transparent window responsible for the shortened transmission signal. We also propose using fluorescence induced by the incident beam as an alternative source to achieve shorter x-ray pulses. Intense femtosecond x rays are valuable to probe the structure and dynamics of biological samples or to reach extreme states of matter. Shortened pulses could be relevant for emerging imaging techniques.

Statistical analysis of hard X-ray radiation at the PAL-XFEL facility performed by Hanbury Brown and Twiss interferometry

A Hanbury Brown and Twiss interferometry experiment based on second-order correlations was performed at the PAL-XFEL facility. The statistical properties of the X-ray radiation were studied within this experiment. Measurements were performed at the NCI beamline at 10 keV photon energy under various operation conditions: self-amplified spontaneous emission (SASE), SASE with a monochromator, and self-seeding regimes at 120 pC, 180 pC and 200 pC electron bunch charge. Statistical analysis showed short average pulse duration from 6 fs to 9 fs depending on the operational conditions. A high spatial degree of coherence of about 70-80% was determined in the spatial domain for the SASE beams with the monochromator and self-seeding regime of operation. The obtained values describe the statistical properties of the beams generated at the PAL-XFEL facility.

Artificial intelligence for online characterization of ultrashort X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) as the world’s brightest light sources provide ultrashort X-ray pulses with a duration typically in the order of femtoseconds. Recently, they have approached and entered the attosecond regime, which holds new promises for single-molecule imaging and studying nonlinear and ultrafast phenomena such as localized electron dynamics. The technological evolution of XFELs toward well-controllable light sources for precise metrology of ultrafast processes has been, however, hampered by the diagnostic capabilities for characterizing X-ray pulses at the attosecond frontier. In this regard, the spectroscopic technique of photoelectron angular streaking has successfully proven how to non-destructively retrieve the exact time–energy structure of XFEL pulses on a single-shot basis. By using artificial intelligence techniques, in particular convolutional neural networks, we here show how this technique can be leveraged from its proof-of-principle stage toward routine diagnostics even at high-repetition-rate XFELs, thus enhancing and refining their scientific accessibility in all related disciplines.

Saturable Absorption of Free-Electron Laser Radiation by Graphite near the Carbon K-Edge

The interaction of intense light with matter gives rise to competing nonlinear responses that can dynamically change material properties. Prominent examples are saturable absorption (SA) and two-photon absorption (TPA), which dynamically increase and decrease the transmission of a sample depending on pulse intensity, respectively. The availability of intense soft X-ray pulses from free-electron lasers (FELs) has led to observations of SA and TPA in separate experiments, leaving open questions about the possible interplay between and relative strength of the two phenomena. Here, we systematically study both phenomena in one experiment by exposing graphite films to soft X-ray FEL pulses of varying intensity. By applying real-time electronic structure calculations, we find that for lower intensities the nonlinear contribution to the absorption is dominated by SA attributed to ground-state depletion; our model suggests that TPA becomes more dominant for larger intensities (>10¹⁴ W/cm²). Our results demonstrate an approach of general utility for interpreting FEL spectroscopies.

Chemical effects on the dynamics of organic molecules irradiated with high intensity x rays

The interaction of a high intensity x-ray pulse with matter causes ionization of the constituent atoms through various atomic processes, and the system eventually goes through a complex structural dynamics. Understanding this whole process is important from the perspective of structure determination of molecules using single particle imaging. XMDYN, which is a classical molecular dynamics-Monte Carlo based hybrid approach, has been successful in simulating the dynamical evolution of various systems under intense irradiation over the past years. The present study aims for extending the XMDYN toolkit to treat chemical bonds using the reactive force field. In order to study its impact, a highly intense x-ray pulse was made to interact with the simplest amino acid, glycine. Different model variants were used to highlight the consequences of charge rearrangement and chemical bonds on the time evolution. The charge-rearrangement-enhanced x-ray ionization of molecules effect is also discussed to address the capability of a classical MD based approach, i.e., XMDYN, to capture such a molecular phenomenon.

Observation of Rabi dynamics with a short-wavelength free-electron laser

Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field1. They are ubiquitous in physics with applications in different areas such as photonics2, nano-electronics3, electron microscopy4 and quantum information5. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interactions within the rotating-wave approximation6. Although intense nanometre-wavelength light sources have been available for more than a decade7-9, Rabi dynamics at such short wavelengths has not been directly observed. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser10 can drive Rabi dynamics between the ground state and an excited state in helium atoms. The measured photoelectron signal reveals an Autler-Townes doublet and an avoided crossing, phenomena that are both fundamental to coherent atom-field interactions11. Using an analytical model derived from perturbation theory on top of the Rabi model, we find that the ultrafast build-up of the doublet structure carries the signature of a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond12 and few-femtosecond13 extreme-ultraviolet pulses, our results unfold opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.

Probing C60 Fullerenes from within Using Free Electron Lasers

Fullerenes, such as C60, are ideal systems to investigate energy redistribution following substantial excitation. Ultra-short and ultra-intense free electron lasers (FELs) have allowed molecular research in a new photon energy regime. FELs have allowed the study of the response of fullerenes to X-rays, which includes femtosecond multi-photon processes, as well as time-resolved ionization and fragmentation dynamics. This perspective: (1) provides a general introduction relevant to C60 research using photon sources, (2) reports on two specific X-ray FEL-based photoionization investigations of C60, at two different FEL fluences, one static and one time-resolved, and (3) offers a brief analysis and recommendations for future research.

The time-resolved atomic, molecular and optical science instrument at the Linac Coherent Light Source

The newly constructed time-resolved atomic, molecular and optical science instrument (TMO) is configured to take full advantage of both linear accelerators at SLAC National Accelerator Laboratory, the copper accelerator operating at a repetition rate of 120 Hz providing high per-pulse energy as well as the superconducting accelerator operating at a repetition rate of about 1 MHz providing high average intensity. Both accelerators power a soft X-ray free-electron laser with the new variable-gap undulator section. With this flexible light source, TMO supports many experimental techniques not previously available at LCLS and will have two X-ray beam focus spots in line. Thereby, TMO supports atomic, molecular and optical, strong-field and nonlinear science and will also host a designated new dynamic reaction microscope with a sub-micrometer X-ray focus spot. The flexible instrument design is optimized for studying ultrafast electronic and molecular phenomena and can take full advantage of the sub-femtosecond soft X-ray pulse generation program.

Benchmark relativistic delta-coupled-cluster calculations of K-edge core-ionization energies of third-row elements

A benchmark computational study of K-edge core-ionization energies of third-row elements using relativistic delta-coupled-cluster (ΔCC) methods and a revised core-valence separation (CVS) scheme is reported. High-level relativistic (HLR) corrections beyond the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), including the contributions from two-electron picture-change effects, spin-orbit coupling, the Breit term, and quantum electrodynamics effects, have been taken into account and demonstrated to play an important role. Relativistic ΔCC calculations are shown to provide accurate results for core-ionization energies of third-row elements. The SFX2C-1e-CVS-ΔCC results augmented with HLR corrections show a maximum deviation of less than 0.5 eV with respect to experimental values.

High-resolution electron time-of-flight spectrometers for angle-resolved measurements at the SQS Instrument at the European XFEL

A set of electron time-of-flight spectrometers for high-resolution angle-resolved spectroscopy was developed for the Small Quantum Systems (SQS) instrument at the SASE3 soft X-ray branch of the European XFEL. The resolving power of this spectrometer design is demonstrated to exceed 10 000 (E/ΔE), using the well known Ne 1s-13p resonant Auger spectrum measured at a photon energy of 867.11 eV at a third-generation synchrotron radiation source. At the European XFEL, a width of ∼0.5 eV full width at half-maximum for a kinetic energy of 800 eV was demonstrated. It is expected that this linewidth can be reached over a broad range of kinetic energies. An array of these spectrometers, with different angular orientations, is tailored for the Atomic-like Quantum Systems endstation for high-resolution angle-resolved spectroscopy of gaseous samples.

A Reaction Microscope for AMO Science at Shanghai Soft X-ray Free-Electron Laser Facility

We report on the design and capabilities of a reaction microscope (REMI) end-station at the Shanghai Soft X-ray Free-Electron Laser Facility (SXFEL). This apparatus allows high-resolution and 4π solid-angle coincidence detection of ions and electrons. The components of REMI, including a supersonic gas injection system, spectrometer, detectors and data acquisition system, are described in detail. By measuring the time of flight and the impact positions of ions and electrons on the corresponding detectors, three-dimensional momentum vectors can be reconstructed to study specific reaction processes. Momentum resolutions of ions and electrons with 0.11 a.u. are achieved, which have been measured from a single ionization experiment of oxygen molecules in an infrared (IR), femtosecond laser field, under vacuum at 1.2×10−10 torr, in a reaction chamber. As a demonstration, a Coulomb explosion experiment of oxygen molecules in the IR field is presented. These results demonstrate the performance of this setup, which provides a basic tool for the study of atomic and molecular reactions at SXFEL.

Approaching the Attosecond Frontier of Dynamics in Matter with the Concept of X-ray Chronoscopy

X-ray free electron lasers (XFELs) have provided scientists opportunities to study matter with unprecedented temporal and spatial resolutions. However, access to the attosecond domain (i.e., below 1 femtosecond) remains elusive. Herein, a time-dependent experimental concept is theorized, allowing us to track ultrafast processes in matter with sub-fs resolution. The proposed X-ray chronoscopy approach exploits the state-of-the-art developments in terahertz streaking to measure the time structure of X-ray pulses with ultrahigh temporal resolution. The sub-femtosecond dynamics of the saturable X-ray absorption process is simulated. The employed rate equation model confirms that the X-ray-induced mechanisms leading to X-ray transparency can be probed via measurement of an X-ray pulse time structure.

Explanation of the anomalous redshift on a nonlinear X-ray Compton scattering spectrum by a bound electron

Nonlinear Compton scattering is an inelastic scattering process where a photon is emitted due to the interaction between an electron and an intense laser field. With the development of X-ray free-electron lasers, the intensity of X-ray laser is greatly enhanced, and the signal from X-ray nonlinear Compton scattering is no longer weak. Although the nonlinear Compton scattering by an initially free electron has been thoroughly investigated, the mechanism of nonrelativistic nonlinear Compton scattering of X-ray photons by bound electrons is unclear yet. Here, we present a frequency-domain formulation based on the nonperturbative quantum electrodynamics to study nonlinear Compton scattering of two photons by an atom in a strong X-ray laser field. In contrast to previous theoretical works, our results clearly reveal the existence of a redshift phenomenon observed experimentally by Fuchs et al.(Nat. Phys.)11, 964(2015) and suggest its origin as the binding energy of the electron as well as the momentum transfer from incident photons to the electron during the scattering process. Our work builds a bridge between intense-laser atomic physics and Compton scattering processes that can be used to study atomic structure and dynamics at high laser intensities.

Investigating charge-up and fragmentation dynamics of oxygen molecules after interaction with strong X-ray free-electron laser pulses

The X-ray-induced charge-up and fragmentation process of a small molecule is examined in great detail by measuring the molecular-frame photoelectron interference pattern in conjunction with other observables in coincidence.

Resonance-Enhanced Multiphoton Ionization in the X-Ray Regime

Here, we report on the nonlinear ionization of argon atoms in the short wavelength regime using ultraintense x rays from the European XFEL. After sequential multiphoton ionization, high charge states are obtained. For photon energies that are insufficient to directly ionize a 1s electron, a different mechanism is required to obtain ionization to Ar^{17+}. We propose this occurs through a two-color process where the second harmonic of the FEL pulse resonantly excites the system via a 1s→2p transition followed by ionization by the fundamental FEL pulse, which is a type of x-ray resonance-enhanced multiphoton ionization (REMPI). This resonant phenomenon occurs not only for Ar^{16+}, but also through lower charge states, where multiple ionization competes with decay lifetimes, making x-ray REMPI distinctive from conventional REMPI. With the aid of state-of-the-art theoretical calculations, we explain the effects of x-ray REMPI on the relevant ion yields and spectral profile.

Effects of x-ray free-electron laser pulse intensity on the Mn K 1,3 x-ray emission spectrum in photosystem II-A case study for metalloprotein crystals and solutions

In the last ten years, x-ray free-electron lasers (XFELs) have been successfully employed to characterize metalloproteins at room temperature using various techniques including x-ray diffraction, scattering, and spectroscopy. The approach has been to outrun the radiation damage by using femtosecond (fs) x-ray pulses. An example of an important and damage sensitive active metal center is the Mn4CaO5 cluster in photosystem II (PS II), the catalytic site of photosynthetic water oxidation. The combination of serial femtosecond x-ray crystallography and Kβ x-ray emission spectroscopy (XES) has proven to be a powerful multimodal approach for simultaneously probing the overall protein structure and the electronic state of the Mn4CaO5 cluster throughout the catalytic (Kok) cycle. As the observed spectral changes in the Mn4CaO5 cluster are very subtle, it is critical to consider the potential effects of the intense XFEL pulses on the Kβ XES signal. We report here a systematic study of the effects of XFEL peak power, beam focus, and dose on the Mn Kβ1,3 XES spectra in PS II over a wide range of pulse parameters collected over seven different experimental runs using both microcrystal and solution PS II samples. Our findings show that for beam intensities ranging from ∼5 × 1015 to 5 × 1017 W/cm2 at a pulse length of ∼35 fs, the spectral effects are small compared to those observed between S-states in the Kok cycle. Our results provide a benchmark for other XFEL-based XES studies on metalloproteins, confirming the viability of this approach.

Transient Valence Charge Localization in Strong-Field Dissociative Ionization of HCl Molecules

Probing transient charge localization in the innershell orbital of atoms and molecules has been made possible by the recent progress of advanced light sources. Here, we demonstrate that the ultrafast electron tunneling ionization by an intense femtosecond laser pulse could induce an asymmetric transient charge localization in the valence shell of the HCl molecule during the dissociative ionization process. The transient charge localization is encoded in the laser impulse acquired by the outgoing ionic fragments, and the asymmetry is revealed by carefully examining the electron tunneling-site distinguished momentum angular distribution of the ejected H^{+} fragments. Our work proposes a way to visualize the transient valence charge motion and will stimulate further investigations of the tunneling-site-sensitive ultrafast dynamics of molecules in strong laser fields.

Pulse Energy and Pulse Duration Effects in the Ionization and Fragmentation of Iodomethane by Ultraintense Hard X Rays

The interaction of intense femtosecond x-ray pulses with molecules sensitively depends on the interplay between multiple photoabsorptions, Auger decay, charge rearrangement, and nuclear motion. Here, we report on a combined experimental and theoretical study of the ionization and fragmentation of iodomethane (CH_{3}I) by ultraintense (∼10^{19}  W/cm^{2}) x-ray pulses at 8.3 keV, demonstrating how these dynamics depend on the x-ray pulse energy and duration. We show that the timing of multiple ionization steps leading to a particular reaction product and, thus, the product's final kinetic energy, is determined by the pulse duration rather than the pulse energy or intensity. While the overall degree of ionization is mainly defined by the pulse energy, our measurement reveals that the yield of the fragments with the highest charge states is enhanced for short pulse durations, in contrast to earlier observations for atoms and small molecules in the soft x-ray domain. We attribute this effect to a decreased charge transfer efficiency at larger internuclear separations, which are reached during longer pulses.

New mounting mechanism for cryogenically cooled thin crystal x-ray optics in high brightness high repetition rate free-electron laser applications

We present a new mounting design for thin crystal optics with cryogenic cooling compatibility. We design a crystal geometry with two symmetric strain-relief cuts to mitigate the distortion from mounting. We propose to sputter gold onto the crystal and the holder to ensure excellent thermal contact and sufficient mechanical bonding. The system is analyzed and verified by finite element analysis to have an acceptable level of strain due to mounting. The thermal performance of this mounting scheme is validated in an example cryogenic cooling system and the results indicate a tolerance of power density up to ∼1 kW/mm².

Fluorescence intensity correlation imaging with high spatial resolution and elemental contrast using intense x-ray pulses

We theoretically investigate the fluorescence intensity correlation (FIC) of Ar clusters and Mo-doped iron oxide nanoparticles subjected to intense, femtosecond, and sub-femtosecond x-ray free-electron laser pulses for high-resolution and elemental contrast imaging. We present the FIC of K α and K α h emission in Ar clusters and discuss the impact of sample damage on retrieving high-resolution structural information and compare the obtained structural information with those from the coherent diffractive imaging (CDI) approach. We found that, while sub-femtosecond pulses will substantially benefit the CDI approach, few-femtosecond pulses may be sufficient for achieving high-resolution information with the FIC. Furthermore, we show that the fluorescence intensity correlation computed from the fluorescence of the Mo atoms in Mo-doped iron oxide nanoparticles can be used to image dopant distributions in the nonresonant regime.

Ultraviolet Pump-Probe Photodissociation Spectroscopy of Electron-Rotation Coupling in Diatomics

The electronic angular momentum projected onto the diatomic axis couples with the angular momentum of the nuclei, significantly affecting the rotational motion of the system under electronic excitations by intense lasers. In this letter, we propose a pump-probe photodissociation scheme for an accurate determination of electron-rotation coupling effects induced by the strong fields. As a showcase we study the CH⁺ molecule excited by a short intense ultraviolet pump pulse to the A¹Π state, which triggers coupled rovibrational dynamics. The dynamics is observed by measuring the kinetic energy release and angular resolved photofragmentation upon photodissociation induced by the time-delayed probe pulse populating the C¹Σ⁺ state. Simulations of the rovibrational dynamics unravel clear fingerprints of the electron-rotation coupling effects that can be observed experimentally. The proposed pump-probe scheme opens new possibilities for the study of ultrafast dynamics following valence electronic transitions with current laser technology, and possible applications are also discussed.

Attosecond pump-attosecond probe spectroscopy of Auger decay

Attosecond pump-attosecond probe spectroscopy is becoming possible due the development of sub-femtosecond free electron laser (FEL) pulses as well as intense high-order harmonic generation-based attosecond sources. Here we investigate theoretically whether these developments can provide access to direct time-resolved measurement of Auger decay through detection of the total yield of an ionic decay product, in analogy to the photodissociation product detection in femtochemistry. We show that the ion yield based measurement is generally possible and in the case of the inner-valence hole decay can be background-free. Extensive first principles calculations are used to optimise the probe photon energies for a variety of prototypical systems.

Features and futures of X-ray free-electron lasers

Linear accelerator-based free-electron lasers (FELs) are the leading source of fully coherent X-rays with ultra-high peak powers and ultra-short pulse lengths. Current X-ray FEL facilities have proved their worth as useful tools for diverse scientific applications. In this paper, we present an overview of the features and future prospects of X-ray FELs, including the working principles and properties of X-ray FELs, the operational status of different FEL facilities worldwide, the applications supported by such facilities, and the current developments and outlook for X-ray FEL-based research.

Ultraintense, ultrashort pulse X-ray scattering in small molecules

We examine X-ray scattering from an isolated organic molecule from the linear to nonlinear absorptive regime. In the nonlinear regime, we explore the importance of both the coherent and incoherent channels and observe the onset of nonlinear behavior as a function of pulse duration and energy. In the linear regime, we test the sensitivity of the scattering signal to molecular bonding and electronic correlation via calculations using the independent atom model (IAM), Hartree-Fock (HF) and density functional theory (DFT). Finally, we describe how coherent X-ray scattering can be used to directly visualize femtosecond charge transfer and dissociation within a single molecule undergoing X-ray multiphoton absorption.

Using X-ray free-electron lasers for spectroscopy of molecular catalysts and metalloenzymes

The metal centres in metalloenzymes and molecular catalysts are responsible for the rearrangement of atoms and electrons during complex chemical reactions, and they enable selective pathways of charge and spin transfer, bond breaking/making and the formation of new molecules. Mapping the electronic structural changes at the metal sites during the reactions gives a unique mechanistic insight that has been difficult to obtain to date. The development of X-ray free-electron lasers (XFELs) enables powerful new probes of electronic structure dynamics to advance our understanding of metalloenzymes. The ultrashort, intense and tunable XFEL pulses enable X-ray spectroscopic studies of metalloenzymes, molecular catalysts and chemical reactions, under functional conditions and in real time. In this Technical Review, we describe the current state of the art of X-ray spectroscopy studies at XFELs and highlight some new techniques currently under development. With more XFEL facilities starting operation and more in the planning or construction phase, new capabilities are expected, including high repetition rate, better XFEL pulse control and advanced instrumentation. For the first time, it will be possible to make real-time molecular movies of metalloenzymes and catalysts in solution, while chemical reactions are taking place.

Atomic-Scale Visualization of Ultrafast Bond Breaking in X-Ray-Excited Diamond

Ultrafast changes of charge density distribution in diamond after irradiation with an intense x-ray pulse (photon energy, 7.8 keV; pulse duration, 6 fs; intensity, 3×10^{19}  W/cm^{2}) have been visualized with the x-ray pump-x-ray probe technique. The measurement reveals that covalent bonds in diamond are broken and the electron distribution around each atom becomes almost isotropic within ∼5  fs after the intensity maximum of the x-ray pump pulse. The 15 fs time delay observed between the bond breaking and atomic disordering indicates nonisothermality of electron and lattice subsystems on this timescale. From these observations and simulation results, we interpret that the x-ray-induced change of the interatomic potential drives the ultrafast atomic disordering underway to the following nonthermal melting.

Extending the Photon Energy Coverage of a Seeded Free-Electron Laser via Reverse Taper Enhanced Harmonic Cascade

External seeded free-electron lasers (FELs) hold promising prospects for producing intense coherent radiation at high harmonics of a conventional laser. The practical harmonic up-conversion efficiencies of current seeding techniques are limited by various three-dimensional effects on the electron beam. In this paper, a novel method is proposed to extend the wavelength coverage of a seeded FEL by combining the reverse taper undulator with the echo-enabled harmonic generation. The proposed technique can significantly enhance the bunching at ultra-high harmonics and preserve the electron beam qualities from degradation by deleterious effects. Theoretical analysis and numerical simulation are performed, and the results demonstrate that stable, intense, nearly fully coherent FEL pulses with photon energy up to 1 keV can be generated. The proposed technique may open up new opportunities to obtain laser-like pulses at sub-nanometer wavelength.

Measuring the frequency chirp of extreme-ultraviolet free-electron laser pulses by transient absorption spectroscopy

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.

Free-electron laser pulses generated from self-amplification of spontaneous emission scheme vary from one another in their characteristics. Here the authors demonstrate a transient absorption spectroscopy method to characterize the frequency chirp of the FEL pulses.

Electron-ion coincidence measurements of molecular dynamics with intense X-ray pulses

Molecules can sequentially absorb multiple photons when irradiated by an intense X-ray pulse from a free-electron laser. If the time delay between two photoabsorption events can be determined, this enables pump-probe experiments with a single X-ray pulse, where the absorption of the first photon induces electronic and nuclear dynamics that are probed by the absorption of the second photon. Here we show a realization of such a single-pulse X-ray pump-probe scheme on N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2 molecules, using the X-ray induced dissociation process as an internal clock that is read out via coincident detection of photoelectrons and fragment ions. By coincidence analysis of the kinetic energies of the ionic fragments and photoelectrons, the transition from a bound molecular dication to two isolated atomic ions is observed through the energy shift of the inner-shell electrons. Via ab-initio simulations, we are able to map characteristic features in the kinetic energy release and photoelectron spectrum to specific delay times between photoabsorptions. In contrast to previous studies where nuclear motions were typically revealed by measuring ion kinetics, our work shows that inner-shell photoelectron energies can also be sensitive probes of nuclear dynamics, which adds one more dimension to the study of light-matter interactions with X-ray pulses.

Two-stage reflective self-seeding scheme for high-repetition-rate X-ray free-electron lasers

X-ray free-electron lasers (XFELs) open a new era of X-ray based research by generating extremely intense X-ray flashes. To further improve the spectrum brightness, a self-seeding FEL scheme has been developed and demonstrated experimentally. As the next step, new-generation FELs with high repetition rates are being designed, built and commissioned around the world. A high repetition rate would significantly speed up the scientific research; however, alongside this improvement comes new challenges surrounding thermal management of the self-seeding monochromator. In this paper, a new configuration for self-seeding FELs is proposed, operated under a high repetition rate which can strongly suppress the thermal effects on the monochromator and provides a narrow-bandwidth FEL pulse. Three-dimension time-dependent simulations have been performed to demonstrate this idea. With this proposed configuration, high-repetition-rate XFEL facilities are able to generate narrow-bandwidth X-ray pulses without obvious thermal concern on the monochromators.