Coherent ultrafast core-hole correlation spectroscopy: x-ray analogues of multidimensional NMR

X-ray/Extreme Ultraviolet Floquet State Multidimensional Spectroscopy, an Analogue of Multiple Quantum Nuclear Magnetic Resonance

There is great interest in developing fully coherent multidimensional X-ray/extreme ultraviolet (XUV) spectroscopic techniques because of their capability for achieving atomic spectral selectivity. Current proposals rest on using sequentially and coherently driven core excitations with multiple X-ray/XUV excitation pulses and measuring the output using time domain Fourier transform methods. In this paper, we propose an alternative method that creates an entanglement of core and optical transitions to form a Floquet state that creates directional and coherent output beams. Multidimensional spectra are obtained by measuring the intensity of output beams while tuning the optical frequencies across resonances. This approach expands on previous optical pump-XUV probe spectroscopy of MoTe₂ by theoretically demonstrating its multidimensional capabilities. Both parametric and non-parametric pathways are proposed to optimize the resolution of inhomogeneous broadening and k-selective features.

Recovering the phase and amplitude of X-ray FEL pulses using neural networks and differentiable models

Dynamics experiments are an important use-case for X-ray free-electron lasers (XFELs), but time-domain measurements of the X-ray pulses themselves remain a challenge. Shot-by-shot X-ray diagnostics could enable a new class of simpler and potentially higher-resolution pump-probe experiments. Here, we report training neural networks to combine low-resolution measurements in both the time and frequency domains to recover X-ray pulses at high-resolution. Critically, we also recover the phase, opening the door to coherent-control experiments with XFELs. The model-based generative neural-network architecture can be trained directly on unlabeled experimental data and is fast enough for real-time analysis on the new generation of MHz XFELs.

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.

An assessment of different electronic structure approaches for modeling time-resolved x-ray absorption spectroscopy

We assess the performance of different protocols for simulating excited-state x-ray absorption spectra. We consider three different protocols based on equation-of-motion coupled-cluster singles and doubles, two of them combined with the maximum overlap method. The three protocols differ in the choice of a reference configuration used to compute target states. Maximum-overlap-method time-dependent density functional theory is also considered. The performance of the different approaches is illustrated using uracil, thymine, and acetylacetone as benchmark systems. The results provide guidance for selecting an electronic structure method for modeling time-resolved x-ray absorption spectroscopy.

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.

Probing Delocalized Current Densities in Selenophene by Resonant X-ray Sum-Frequency Generation

Time-resolved, resonant X-ray sum-frequency generation in aligned selenophene molecules is calculated. A wave packet of valence-excited states, prepared by an extreme-ultraviolet pump pulse, is probed by two 12-keV X-ray probe pulses resonant with the Se core-excited states for variable time delays. At these hard-X-ray frequencies, the angström wavelength of the X-ray probe is comparable to the molecular size. We thus employ a nonlocal description of the light-matter interaction based on the minimal-coupling Hamiltonian. The wavevector-resolved resonant stimulated sum-frequency-generation signal, obtained by varying the propagation direction of hard-X-ray pulses, can thus directly monitor the transition current densities between core and ground/valence states. This is in contrast to off-resonant diffraction, which detects the transition charge densities.

Intense x-rays can be (slightly) exciting

Imaging of neutral “survivor” atoms excited by x-ray blasts fights radiation damage

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Selective Elimination of Homogeneous Broadening by Multidimensional Spectroscopy in the Electromagnetically Induced Transparency Regime

The key feature of photon echo-based spectroscopies is a selective elimination of the inhomogeneous broadening. Fast homogeneous dephasing typical for large macromolecules makes it difficult to resolve the congested spectra even if the inhomogeneous component is eliminated. We propose a novel two-dimensional spectroscopy in which a series of temporally separated probe pulses are combined with the strong narrowband control pulse. Using electromagnetically induced transparency originating from the interference between the control and probe pulses, we achieve an observation window for molecular response in narrow spectral intervals significantly smaller than the homogeneous dephasing limit.

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.

Nonlinear Coherence Effects in Transient-Absorption Ion Spectroscopy with Stochastic Extreme-Ultraviolet Free-Electron Laser Pulses

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.

Stable interferometric platform for phase modulation of seeded free-electron lasers

We present a compact phase modulation setup designed for high laser intensities sufficient to drive highly nonlinear processes, such as high-gain harmonic generation in seeded free-electron lasers. This paves the way for all-extreme-ultravioloet coherent nonlinear spectroscopy. The high linearity, phase stability, and sensitivity of the setup are demonstrated by probing the quantum interference of electronic wave packets in the deep ultraviolet region (268 nm) combined with photoion time-of-flight mass spectrometry.

Two-dimensional UV spectroscopy: a new insight into the structure and dynamics of biomolecules

Two-dimensional ultraviolet spectroscopy has the potential to deliver rich structural and dynamical information on biomolecules such as DNA and proteins.

Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by [Formula: see text]. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures [Formula: see text] where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid [Formula: see text]He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.

Study of double core hole excitations in molecules by X-ray double-quantum-coherence signals: a multi-configuration simulation

The multi-configurational self-consistent field method is employed to simulate the two-dimensional all-X-ray double-quantum-coherence (XDQC) spectroscopy, a four-wave mixing signal that provides direct signatures of double core hole (DCH) states. The valence electronic structure is probed by capturing the correlation between the single (SCH) and double core hole states. The state-averaged restricted-active-space self-consistent field (SA-RASSCF) approach is used which can treat the valence, SCH, and DCH states at the same theoretical level, and applies to all types of DCHs (located on one or two atoms, K-edge or L-edge), with both accuracy and efficiency. Orbital relaxation introduced by the core hole(s) and the static electron correlation is properly accounted for. The XDQC process can take place via different intermediate DCH state channels by tuning the pulse frequencies. We simulate the XDQC signals for the three isomers of aminophenol at 8 pulse frequency configurations, covering all DCH pathways involving the N1s and O1s core hole (N1sN1s, O1sO1s and N1sO1s), which reveal different patterns of valence excitations.

Curved gratings as an integrated photon fluence monitor in x-ray transmission scattering experiments

A concept to obtain a measure of the photon flux accepted by a solid sample in single-shot transmission experiments with extreme ultraviolet (XUV) or soft x-ray radiation is demonstrated. Shallow, continuously distorted gratings are used to diffract a constant fraction of the incident photons onto an extended area of a CCD detector. The signal can be tailored to fit the dynamic range of the detector, i.e. matching the scattered intensity of the studied structure of interest. Furthermore, composite grating designs that also allow for the measurement of the spatial photon distribution on the sample are demonstrated. The gratings are directly fabricated by focused ion-beam (FIB) lithography into a Si₃N₄ membrane that supports the actual sample layer. This allows for rapid fabrication of hundreds of samples, making the concept suitable for systematic studies in destructive single-shot measurements at free-electron laser (FEL) sources. We demonstrate relative photon flux measurements in magnetic scattering experiments with synchrotron and FEL radiation at 59.6 eV photon energy.

Time-resolved four-wave-mixing spectroscopy for inner-valence transitions

Noncollinear four-wave-mixing (FWM) techniques at near-infrared (NIR), visible, and ultraviolet frequencies have been widely used to map vibrational and electronic couplings, typically in complex molecules. However, correlations between spatially localized inner-valence transitions among different sites of a molecule in the extreme ultraviolet (XUV) spectral range have not been observed yet. As an experimental step toward this goal, we perform time-resolved FWM spectroscopy with femtosecond NIR and attosecond XUV pulses. The first two pulses (XUV-NIR) coincide in time and act as coherent excitation fields, while the third pulse (NIR) acts as a probe. As a first application, we show how coupling dynamics between odd- and even-parity, inner-valence excited states of neon can be revealed using a two-dimensional spectral representation. Experimentally obtained results are found to be in good agreement with ab initio time-dependent R-matrix calculations providing the full description of multielectron interactions, as well as few-level model simulations. Future applications of this method also include site-specific probing of electronic processes in molecules.

Attosecond science in atomic, molecular, and condensed matter physics

Attosecond science represents a new frontier in atomic, molecular, and condensed matter physics, enabling one to probe the exceedingly fast dynamics associated with purely electronic dynamics in a wide range of systems. This paper presents a brief discussion of the technology required to generate attosecond light pulses and gives representative examples of attosecond science carried out in several laboratories. Attosecond transient absorption, a very powerful method in attosecond science, is then reviewed and several examples of gas phase and condensed phase experiments that have been carried out in the Leone/Neumark laboratories are described.

Spectrotemporal shaping of seeded free-electron laser pulses

We demonstrate the ability to control and shape the spectrotemporal content of extreme-ultraviolet (XUV) pulses produced by a seeded free-electron laser (FEL). The control over the spectrotemporal properties of XUV light was achieved by precisely manipulating the linear frequency chirp of the seed laser. Our results agree with existing theory, which allows us to retrieve the temporal properties (amplitude and phase) of the FEL pulse from measurements of the spectra as a function of the FEL operating parameters. Furthermore, we show the first direct evidence of the full temporal coherence of FEL light and generate Fourier limited pulses by fine-tuning the FEL temporal phase. The possibility of tailoring the spectrotemporal content of intense short-wavelength pulses represents the first step towards efficient nonlinear optics in the XUV to x-ray spectral region and will enable precise manipulation of core-electron excitations using the methods of coherent quantum control.

Single-shot spectro-temporal characterization of XUV pulses from a seeded free-electron laser

Intense ultrashort X-ray pulses produced by modern free-electron lasers (FELs) allow one to probe biological systems, inorganic materials and molecular reaction dynamics with nanoscale spatial and femtoscale temporal resolution. These experiments require the knowledge, and possibly the control, of the spectro-temporal content of individual pulses. FELs relying on seeding have the potential to produce spatially and temporally fully coherent pulses. Here we propose and implement an interferometric method, which allows us to carry out the first complete single-shot spectro-temporal characterization of the pulses, generated by an FEL in the extreme ultraviolet spectral range. Moreover, we provide the first direct evidence of the temporal coherence of a seeded FEL working in the extreme ultraviolet spectral range and show the way to control the light generation process to produce Fourier-limited pulses. Experiments are carried out at the FERMI FEL in Trieste.

Transient impulsive electronic Raman redistribution

Resonant Raman excitation by ultrafast vacuum ultraviolet laser pulses is a powerful means to study electron dynamics in molecules, but experiments must contend with linear background ionization: frequencies high enough to reach resonant core-valence transitions will usually ionize all occupied orbitals as well, and the ionization cross sections are usually dominant. Here we show that attosecond pulses can induce a process, transient impulsive stimulated Raman scattering, which can overwhelm valence ionization. Calculations are performed for atomic sodium, but the principal is valid for many molecular systems. This approach opens the path for high-fidelity multidimensional spectroscopy with attosecond pulses.

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Coherent multidimensional optical spectra measured using incoherent light

Four-wave mixing measurements can reveal spectral and dynamics information that is hidden in linear spectra by the interactions among light-absorbing molecules and with their environment. Coherent multidimensional optical spectroscopy is an important variant of four-wave mixing because it resolves a map of interactions and correlations between absorption bands. Previous coherent multidimensional optical spectroscopy measurements have used femtosecond pulses with great success, and it may seem that femtosecond pulses are necessary for such measurements. Here we present coherent two-dimensional electronic spectra measured using incoherent light. The spectra of model molecular systems using broadband spectrally incoherent light are similar but not identical to those expected from measurements using femtosecond pulses. Specifically, the spectra show particular sensitivity to long-lived intermediates such as photoisomers. The results will motivate the design of similar experiments in spectral ranges where femtosecond pulses are difficult to produce.

Disruptive photon technologies for chemical dynamics

A perspective of new and emerging technologies for chemical dynamics is given, with an emphasis on the use of X-ray sources that generate sub-picosecond pulses. The two classes of experimental techniques used for time-resolved measurements of chemical processes and their effects are spectroscopy and imaging, where the latter includes microscopy, diffractive imaging, and crystallography. X-Ray free-electron lasers have brought new impetus to the field, allowing not only temporal and spatial resolution at atomic time and length scales, but also bringing a new way to overcome limitations due to perturbation of the sample by the X-ray probe by out-running radiation damage. Associated instrumentation and methods are being developed to take advantage of the new opportunities of these sources. Once these methods of observational science have been mastered it should be possible to use the new tools to directly control those chemical processes.

Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy

The attosecond, time-resolved X-ray double-quantum-coherence four-wave mixing signals of formamide at the nitrogen and oxygen K-edges are simulated using restricted excitation window time-dependent density functional theory and the excited core hole approximation. These signals, induced by core exciton coupling, are particularly sensitive to the level of treatment of electron correlation, thus providing direct experimental signatures of electron and core-hole many-body effects and a test of electronic structure theories.

Core and valence excitations in resonant X-ray spectroscopy using restricted excitation window time-dependent density functional theory

We report simulations of X-ray absorption near edge structure (XANES), resonant inelastic X-ray scattering (RIXS) and 1D stimulated X-ray Raman spectroscopy (SXRS) signals of cysteine at the oxygen, nitrogen, and sulfur K and L(2,3) edges. Comparison of the simulated XANES signals with experiment shows that the restricted window time-dependent density functional theory is more accurate and computationally less expensive than the static exchange method. Simulated RIXS and 1D SXRS signals give some insights into the correlation of different excitations in the molecule.

Passively phase-stable, monolithic, all-reflective two-dimensional electronic spectroscopy based on a four-quadrant mirror

A design for a passively phase-stable two-dimensional electronic spectroscopy experiment, based on a four-quadrant mirror concept, is introduced. The setup, which is particularly simple and robust, achieves subwavelength stability without the need for active stabilization or diffractive optical elements. Since only reflective optical components are used, the setup is suitable for few-cycle laser pulses and ultrabroad-bandwidth light in the ultraviolet, visible, and near-IR regions, with the capability to be used under grazing incidence for soft x ray or x-ray light at free-electron lasers.

X-ray and optical wave mixing

Light-matter interactions are ubiquitous, and underpin a wide range of basic research fields and applied technologies. Although optical interactions have been intensively studied, their microscopic details are often poorly understood and have so far not been directly measurable. X-ray and optical wave mixing was proposed nearly half a century ago as an atomic-scale probe of optical interactions but has not yet been observed owing to a lack of sufficiently intense X-ray sources. Here we use an X-ray laser to demonstrate X-ray and optical sum-frequency generation. The underlying nonlinearity is a reciprocal-space probe of the optically induced charges and associated microscopic fields that arise in an illuminated material. To within the experimental errors, the measured efficiency is consistent with first-principles calculations of microscopic optical polarization in diamond. The ability to probe optical interactions on the atomic scale offers new opportunities in both basic and applied areas of science.

Probing Photosynthetic Energy and Charge Transfer with Two-Dimensional Electronic Spectroscopy

Two-dimensional electronic spectroscopy (2DES) has emerged as a powerful method for elucidating the structure-function relationship in photosynthetic systems. In this Perspective, we discuss features of two-dimensional spectroscopy that make it highly suited to address questions about the underlying electronic structure that guides energy- and charge-transfer processes in light-harvesting materials. We briefly describe a pulse-shaping-based implementation of two-dimensional spectroscopy that is making the method widely accessible to problems spanning frequency regimes from the ultraviolet to the mid-infrared. We illustrate the utility of 2DES in the context of our recent studies of the primary energy-transfer and charge separation events in the photosystem II reaction center, discussing remaining challenges and speculating about exciting future directions for the field of multidimensional spectroscopy.

X-ray two-photon photoelectron spectroscopy: a theoretical study of inner-shell spectra of the organic para-aminophenol molecule

The inner-shell single and double ionization spectra of the organic molecule para-aminophenol are calculated using many-body Green's function methods. The inner-shell double ionization spectrum displays more pronounced sensitivity to the chemical environment and to electronic many-body effects than does the inner-shell single ionization spectrum. A kinetic model is employed to determine the probability of inner-shell double hole formation in para-aminophenol exposed to an intense, 1 fs x-ray pulse. The resulting photoelectron spectrum at a photon energy of 1 keV is calculated. This work suggests that x-ray two-photon photoelectron spectroscopy using x-ray free-electron lasers will provide access to electronic-structure information not currently available.