Nonlinear Spectroscopy with X-Ray Two-Photon Absorption in Metallic Copper

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.

Ultrafast spectroscopy of liquids using extreme-ultraviolet to soft-X-ray pulses

Ultrafast X-ray spectroscopy provides access to molecular dynamics with unprecedented time resolution, element specificity and site selectivity. These unique properties are optimally suited for investigating intramolecular and intermolecular interactions of molecular species in the liquid phase. This Review summarizes experimental breakthroughs, such as water photolysis and proton transfer on femtosecond and attosecond time scales, dynamics of solvated electrons, charge-transfer processes in metal complexes, multiscale dynamics in haem proteins, proton-transfer dynamics in prebiotic systems and liquid-phase extreme-ultraviolet high-harmonic spectroscopy. An important novelty for ultrafast liquid-phase spectroscopy is the availability of high-brightness ultrafast short-wavelength sources that allowed access to the water window (from 200 eV to 550 eV) and thus to the K-edges of the key elements of organic and biological chemistry: C, N and O. Not only does this Review present experimental examples that demonstrate the unique capabilities of ultrafast short-wavelength spectroscopy in liquids, but it also highlights the broad range of spectroscopic methodologies already applied in this field.

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.

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.

Spectral-brightness optimization of an X-ray free-electron laser by machine-learning-based tuning

A machine-learning-based beam optimizer has been implemented to maximize the spectral brightness of the X-ray free-electron laser (XFEL) pulses of SACLA. A new high-resolution single-shot inline spectrometer capable of resolving features of the order of a few electronvolts was employed to measure and evaluate XFEL pulse spectra. Compared with a simple pulse-energy-based optimization, the spectral width was narrowed by half and the spectral brightness was improved by a factor of 1.7. The optimizer significantly contributes to efficient machine tuning and improvement of XFEL performance at SACLA.

Single-shot X-ray absorption spectroscopy at X-ray free electron lasers

X-ray Absorption Spectroscopy (XAS) is a widely used X-ray diagnostic method for studying electronic and structural properties of matter. At first glance, the relatively narrow bandwidth and the highly fluctuating spectral structure of X-ray Free Electron Lasers (XFEL) sources seem to require accumulation over many shots to achieve high data quality. To date the best approach to implementing XAS at XFEL facilities has been using monochromators to scan the photon energy across the desired spectral range. While this is possible for easily reproducible samples such as liquids, it is incompatible with many important systems. Here, we demonstrate collection of single-shot XAS spectra over 10s of eV using an XFEL source, with error bars of only a few percent. We additionally show how to extend this technique over wider spectral ranges towards Extended X-ray Absorption Fine Structure measurements, by concatenating a few tens of single-shot measurements. Our results pave the way for future XAS studies at XFELs, in particular those in the femtosecond regime. This advance is envisioned to be especially important for many transient processes that can only be initiated at lower repetition rates, for difficult to reproduce excitation conditions, or for rare samples, such as those encountered in high-energy density physics.

Two-dimensional Kβ-Kα fluorescence spectrum by nonlinear resonant inelastic X-ray scattering

High sensitivity of the Kβ fluorescence spectrum to electronic state is widely used to investigate spin and oxidation state of first-row transition-metal compounds. However, the complex electronic structure results in overlapping spectral features, and the interpretation may be hampered by ambiguity in resolving the spectrum into components representing different electronic states. Here, we tackle this difficulty with a nonlinear resonant inelastic X-ray scattering (RIXS) scheme, where we leverage sequential two-photon absorption to realize an inverse process of the Kβ emission, and measure the successive Kα emission. The nonlinear RIXS reveals two-dimensional (2D) Kβ-Kα fluorescence spectrum of copper metal, leading to better understanding of the spectral feature. We isolate 3d-related satellite peaks in the 2D spectrum, and find good agreement with our multiplet ligand field calculation. Our work not only advances the fluorescence spectroscopy, but opens the door to extend RIXS into the nonlinear regime.

Cherry-Picking Resolvents: Recovering the Valence Contribution in X-ray Two-Photon Absorption within the Core-Valence-Separated Equation-of-Motion Coupled-Cluster Response Theory

Calculations of first-order response wave functions in the X-ray regime often diverge within correlated frameworks such as equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), a consequence of the coupling with the valence ionization continuum. Here, we extend our strategy of introducing a hierarchy of approximations to the EOM-EE-CCSD resolvent (or, inversely, the model Hamiltonian) involved in the response equations for the calculation of X-ray two-photon absorption (X2PA) cross sections. We exploit the frozen-core core-valence separation (fc-CVS) scheme to first decouple the core and valence Fock spaces, followed by a separate approximate treatment of the valence resolvent. We demonstrate the robust convergence of X-ray response calculations within this framework and compare X2PA spectra of small benchmark molecules with the previously reported density functional theory results.

Advances in the OCEAN-3 spectroscopy package

The OCEAN code for calculating valence- and core-level spectra using the Bethe-Salpeter equation is briefly reviewed. OCEAN is capable of calculating optical absorption, near-edge X-ray absorption or non-resonant scattering, and resonant inelastic X-ray scattering, requiring only the structure of the material as input. Improved default behavior and reduced input requirements are detailed as well as new capabilities, such as incorporation of final-state-dependent broadening, finite-temperature dependence, and flexibility in the density-functional theory exchange-correlation potentials. OCEAN is built on top of a plane-wave, pseudopotential, density-functional theory foundation, and calculations are shown for systems ranging in size up to 7 nm3.

Shortening X-Ray Pulse Duration via Saturable Absorption

To shorten the duration of x-ray pulses, we present a nonlinear optical technique using atoms with core-hole vacancies (core-hole atoms) generated by inner-shell photoionization. The weak Coulomb screening in the core-hole atoms results in decreased absorption at photon energies immediately above the absorption edge. By employing this phenomenon, referred to as saturable absorption, we successfully reduce the duration of x-ray free-electron laser pulses (photon energy: 9.000 keV, duration: 6-7 fs, fluence: 2.0-3.5×10^{5}  J/cm^{2}) by ∼35%. This finding that core-hole atoms are applicable to nonlinear x-ray optics is an essential stepping stone for extending nonlinear technologies commonplace at optical wavelengths to the hard x-ray region.

Table-top extreme ultraviolet second harmonic generation

The lack of available table-top extreme ultraviolet (XUV) sources with high enough fluxes and coherence properties has limited the availability of nonlinear XUV and x-ray spectroscopies to free-electron lasers (FELs). Here, we demonstrate second harmonic generation (SHG) on a table-top XUV source by observing SHG near the Ti M_2,3 edge with a high-harmonic seeded soft x-ray laser. Furthermore, this experiment represents the first SHG experiment in the XUV. First-principles electronic structure calculations suggest the surface specificity and separate the observed signal into its resonant and nonresonant contributions. The realization of XUV-SHG on a table-top source opens up more accessible opportunities for the study of element-specific dynamics in multicomponent systems where surface, interfacial, and bulk-phase asymmetries play a driving role.

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.

Two-color X-ray free-electron laser consisting of broadband and narrowband beams

A simple scheme is proposed and experimentally confirmed to generate X-ray free-electron lasers (XFELs) consisting of broadband and narrowband beams with a controllable intensity ratio and a large photon-energy separation. This unique two-color XFEL beam will open new opportunities for investigation of nonlinear interactions between intense X-rays and matter.

Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima

Photoelectron angular distributions of the two-photon ionization of neutral atoms are theoretically investigated. Numerical calculations of two-photon ionization cross sections and asymmetry parameters are carried out within the independent-particle approximation and relativistic second-order perturbation theory. The dependence of the asymmetry parameters on the polarization and energy of the incident light as well as on the angular momentum properties of the ionized electron are investigated. While dynamic variations of the angular distributions at photon energies near intermediate level resonances are expected, we demonstrate that equally strong variations occur near the nonlinear Cooper minimum. The described phenomena is demonstrated on the example of two-photon ionization of magnesium atom.

High-resolution micro channel-cut crystal monochromator processed by plasma chemical vaporization machining for a reflection self-seeded X-ray free-electron laser

A high-resolution micro channel-cut crystal monochromator (µCCM) composed of an Si(220) crystal is developed for the purpose of narrowing the bandwidth of a reflection self-seeded X-ray free-electron laser. Subsurface damage on the monochromator, which distorts the wavefront and broadens the bandwidth of the monochromatic seed beam, was removed by using a plasma etching technique. High diffraction performance of the monochromator was confirmed through evaluation with coherent X-rays. Reflection self-seeding operation was tested with the Si(220) µCCM at SPring-8 Angstrom Compact free-electron laser. A narrow average bandwidth of 0.6 eV, which is five times narrower than the value previously reported [I. Inoue et al., Nat. Photonics13, 319 (2019)10.1038/s41566-019-0365-y], was successfully obtained at 9 keV. The narrow-band X-ray beams with high intensity realized in this study will further expand the capabilities of X-ray free-electron lasers.

Breakdown of the electric dipole approximation at Cooper minima in direct two-photon ionisation

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K–shell atomic ionisation by circularly polarised light. According to predictions based on the electric dipole approximation, we expect that tuning the incident photon energy to the Cooper minimum in two-photon ionisation results in pure depletion of one spin projection of the initially bound 1s electrons, and hence, leaves the ionised atom in a fully oriented state. We show that by inclusion of electric quadrupole interaction, dramatic drop of orientation purity is obtained. The low degree of the remaining ion orientation provides a direct access to contributions of the electron-photon interaction beyond the electric dipole approximation in the two-photon ionisation of atoms and molecules. The orientation of the photoions can be experimentally detected either directly by a Stern-Gerlach analyzer, or by means of subsequent Kα fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons.

Observation of strong nonlinear interactions in parametric down-conversion of X-rays into ultraviolet radiation

Nonlinear interactions between X-rays and long wavelength radiation can be used as a powerful atomic-scale probe for light-matter interactions and for properties of valence electrons. However, reported X-ray nonlinear effects were small and their observations required tremendous efforts. Here we report the observation of strong nonlinearities in parametric down-conversion (PDC) of X-rays to long wavelength radiation in gallium arsenide and lithium niobate crystals, with efficiencies about 4 orders of magnitude stronger than the efficiencies measured in any material studied before. Furthermore, we show that the efficiency in the ferroelectric phase of strontium barium niobite is two orders of magnitude stronger than in its paraelectric phase. This observation suggests that the lack of inversion symmetry is the origin for the strong observed nonlinearity. Additionally, we demonstrate the ability to use the effect for the investigation of the spectral response of non-centrosymmetric materials at wavelengths ranging from infrared to soft X-rays.

Here, the authors report parametric down-conversion of X-rays into long wavelength radiation in gallium arsenide and lithium niobate crystals, with efficiencies about 4 orders of magnitude stronger than the efficiencies measured in any material studied previously. They explore the lack of inversion symmetry as a possible physical mechanism.

Intense sub-micrometre focusing of soft X-ray free-electron laser beyond 1016 W cm-2 with an ellipsoidal mirror

Intense sub-micrometre focusing of a soft X-ray free-electron laser (FEL) was achieved by using an ellipsoidal mirror with a high numerical aperture. A hybrid focusing system in combination with a Kirkpatrick-Baez mirror was applied for compensation of a small spatial acceptance of the ellipsoidal mirror. With this system, the soft X-ray FEL pulses were focused down to 480 nm × 680 nm with an extremely high intensity of 8.8×10¹⁶ W cm^-2 at a photon energy of 120 eV, which yielded saturable absorption at the L-edge of Si (99.8 eV) with a drastic increase of transmittance from 8% to 48%.

Multiple-beamline operation of SACLA

The SPring-8 Ångstrom Compact free-electron LAser (SACLA) began parallel operation of three beamlines (BL1-3) in autumn 2017 to increase the user beam time of the X-ray free-electron laser. The success of the multiple-beamline operation is based on two technological achievements: (i) the fast switching operation of the SACLA main linear accelerator, which provides BL2 and BL3 with pulse-by-pulse electron beams, and (ii) the relocation and upgrade of the SPring-8 Compact SASE Source for BL1, for the generation of a soft X-ray free-electron laser. Moreover, the photon beamlines and experimental stations were upgraded to facilitate concurrent user experiments at the three beamlines and accommodate more advanced experiments.