Efficient prediction of attosecond two-colour pulses from an X-ray free-electron laser with machine learning.

X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes.

Coupled Electron-Nuclear Dynamics Induced and Monitored with Femtosecond Soft X-ray Pulses in the Amino Acid Glycine.

The coupling of electronic and nuclear motion in polyatomic molecules is at the heart of attochemistry. The molecular properties, transient structures, and reaction mechanism of these many-body quantum objects are defined on the level of electrons and ions by molecular wave functions and their coherent superposition, respectively. In the present contribution, we monitor nonadiabatic quantum wave packet dynamics during molecular charge motion by reconstructing both the oscillatory charge density distribution and the characteristic time-dependent nuclear configuration coordinate from time-resolved Auger electron spectroscopic data recorded in previous studies on glycine molecules [Schwickert et al. Sci. Adv. 2022, 8, eabn6848]. The electronic and nuclear motion on the femtosecond time scale was induced and probed in kinematically complete soft X-ray experiments at the FLASH free-electron laser facility. The detailed analysis of amplitude, instantaneous phase, and instantaneous frequency of the propagating many-body wave packet during its lifecycle provides unprecedented insight into dynamical processes beyond the Born-Oppenheimer approximation. We are confident that the refined experimental data evaluation helps to develop new theoretical tools to describe time-dependent molecular wave functions in complicated but ubiquitous non-Born-Oppenheimer photochemical conditions.

Optical control of ultrafast structural dynamics in a fluorescent protein.

The photoisomerization reaction of a fluorescent protein chromophore occurs on the ultrafast timescale. The structural dynamics that result from femtosecond optical excitation have contributions from vibrational and electronic processes and from reaction dynamics that involve the crossing through a conical intersection. The creation and progression of the ultrafast structural dynamics strongly depends on optical and molecular parameters. When using X-ray crystallography as a probe of ultrafast dynamics, the origin of the observed nuclear motions is not known. Now, high-resolution pump-probe X-ray crystallography reveals complex sub-ångström, ultrafast motions and hydrogen-bonding rearrangements in the active site of a fluorescent protein. However, we demonstrate that the measured motions are not part of the photoisomerization reaction but instead arise from impulsively driven coherent vibrational processes in the electronic ground state. A coherent-control experiment using a two-colour and two-pulse optical excitation strongly amplifies the X-ray crystallographic difference density, while it fully depletes the photoisomerization process. A coherent control mechanism was tested and confirmed the wave packets assignment.

Identification of Cofragmented Combinatorial Peptide Isomers by Two-Dimensional Partial Covariance Mass Spectrometry.

Combinatorial post-translational modifications (PTMs), such as those forming the so-called "histone code", have been linked to cell differentiation, embryonic development, cellular reprogramming, aging, cancers, neurodegenerative disorders, etc. Nevertheless, a reliable mass spectral analysis of the combinatorial isomers represents a considerable challenge. The difficulty stems from the incompleteness of information that could be generated by the standard MS to differentiate cofragmented isomeric sequences in their naturally occurring mixtures based on the fragment mass-to-charge ratio and relative abundance information only. Here we show that fragment-fragment correlations revealed by two-dimensional partial covariance mass spectrometry (2D-PC-MS) allow one to solve the combinatorial PTM puzzles that cannot be tackled by the standard MS as a matter of principle. We introduce 2D-PC-MS marker ion correlation approach and demonstrate experimentally that it can provide the missing information enabling identification of cofragmentated combinatorially modified isomers. Our in silico study shows that the marker ion correlations can be used to unambiguously identify 5 times more cofragmented combinatorially acetylated tryptic peptides and 3 times more combinatorially modified Glu-C peptides of human histones than is possible using standard MS methods.

Delivery of stable ultra-thin liquid sheets in vacuum for biochemical spectroscopy.

The development of ultra-thin flat liquid sheets capable of running in vacuum has provided an exciting new target for X-ray absorption spectroscopy in the liquid and solution phases. Several methods have become available for delivering in-vacuum sheet jets using different nozzle designs. We compare the sheets produced by two different types of nozzle; a commercially available borosillicate glass chip using microfluidic channels to deliver colliding jets, and an in-house fabricated fan spray nozzle which compresses the liquid on an axis out of a slit to achieve collision conditions. We find in our tests that both nozzles are suitable for use in X-ray absorption spectroscopy with the fan spray nozzle producing thicker but more stable jets than the commercial nozzle. We also provide practical details of how to run these nozzles in vacuum.

Charge-induced chemical dynamics in glycine probed with time-resolved Auger electron spectroscopy.

In the present contribution, we use x-rays to monitor charge-induced chemical dynamics in the photoionized amino acid glycine with femtosecond time resolution. The outgoing photoelectron leaves behind the cation in a coherent superposition of quantum mechanical eigenstates. Delayed x-ray pulses track the induced coherence through resonant x-ray absorption that induces Auger decay. Temporal modulation of the Auger electron signal correlated with specific ions is observed, which is governed by the initial electronic coherence and subsequent vibronic coupling to nuclear degrees of freedom. In the time-resolved x-ray absorption measurement, we monitor the time-frequency spectra of the resulting many-body quantum wave packets for a period of 175 fs along different reaction coordinates. Our experiment proves that by measuring specific fragments associated with the glycine dication as a function of the pump-probe delay, one can selectively probe electronic coherences at early times associated with a few distinguishable components of the broad electronic wave packet created initially by the pump pulse in the cation. The corresponding coherent superpositions formed by subsets of electronic eigenstates and evolving along parallel dynamical pathways show different phases and time periods in the range of ( - 0.3 ± 0.1 ) π ≤ ϕ ≤ ( 0.1 ± 0.2 ) π and 18.2 - 1.4 + 1.7 ≤ T ≤ 23.9 - 1.1 + 1.2 fs. Furthermore, for long delays, the data allow us to pinpoint the driving vibrational modes of chemical dynamics mediating charge-induced bond cleavage along different reaction coordinates.

How electronic superpositions drive nuclear motion following the creation of a localized hole in the glycine radical cation.

In this work, we have studied the nuclear and electron dynamics in the glycine cation starting from localized hole states using the quantum Ehrenfest method. The nuclear dynamics is controlled both by the initial gradient and by the instantaneous gradient that results from the oscillatory electron dynamics (charge migration). We have used the Fourier transform (FT) of the spin densities to identify the "normal modes" of the electron dynamics. We observe an isomorphic relationship between the electron dynamics normal modes and the nuclear dynamics, seen in the vibrational normal modes. The FT spectra obtained this way show bands that are characteristic of the energy differences between the adiabatic hole states. These bands contain individual peaks that are in one-to-one correspondence with atom pair (+·) ↔ (·+) resonances, which, in turn, stimulate nuclear motion involving the atom pair. With such understanding, we anticipate "designer" coherent superpositions that can drive nuclear motion in a particular direction.

Electronic quantum coherence in glycine molecules probed with ultrashort x-ray pulses in real time.

Here, we use x-rays to create and probe quantum coherence in the photoionized amino acid glycine. The outgoing photoelectron leaves behind the cation in a coherent superposition of quantum mechanical eigenstates. Delayed x-ray pulses track the induced coherence through resonant x-ray absorption that induces Auger decay and by photoelectron emission from sequential double photoionization. Sinusoidal temporal modulation of the detected signal at early times (0 to 25 fs) is observed in both measurements. Advanced ab initio many-electron simulations allow us to explain the first 25 fs of the detected coherent quantum evolution in terms of the electronic coherence. In the kinematically complete x-ray absorption measurement, we monitor its dynamics for a period of 175 fs and observe an evolving modulation that may implicate the coupling of electronic to vibronic coherence at longer time scales. Our experiment provides a direct support for the existence of long-lived electronic coherence in photoionized biomolecules.

Attosecond coherent electron motion in Auger-Meitner decay.

In quantum systems, coherent superpositions of electronic states evolve on ultrafast time scales (few femtoseconds to attoseconds; 1 attosecond = 0.001 femtoseconds = 10-18 seconds), leading to a time-dependent charge density. Here we performed time-resolved measurements using attosecond soft x-ray pulses produced by a free-electron laser, to track the evolution of a coherent core-hole excitation in nitric oxide. Using an additional circularly polarized infrared laser pulse, we created a clock to time-resolve the electron dynamics and demonstrated control of the coherent electron motion by tuning the photon energy of the x-ray pulse. Core-excited states offer a fundamental test bed for studying coherent electron dynamics in highly excited and strongly correlated matter.

Proteomic Database Search Engine for Two-Dimensional Partial Covariance Mass Spectrometry.

We present a protein database search engine for the automatic identification of peptide and protein sequences using the recently introduced method of two-dimensional partial covariance mass spectrometry (2D-PC-MS). Because the 2D-PC-MS measurement reveals correlations between fragments stemming from the same or consecutive decomposition processes, the first-of-its-kind 2D-PC-MS search engine is based entirely on the direct matching of the pairs of theoretical and the experimentally detected correlating fragments, rather than of individual fragment signals or their series. We demonstrate that the high structural specificity afforded by 2D-PC-MS fragment correlations enables our search engine to reliably identify the correct peptide sequence, even from a spectrum with a large proportion of contaminant signals. While for peptides, the 2D-PC-MS correlation-matching procedure is based on complementary and internal ion correlations, the identification of intact proteins is entirely based on the ability of 2D-PC-MS to spatially separate and resolve the experimental correlations between complementary fragment ions.

Two-Dimensional Partial Covariance Mass Spectrometry for the Top-Down Analysis of Intact Proteins.

Two-dimensional partial covariance mass spectrometry (2D-PC-MS) exploits the inherent fluctuations of fragment ion abundances across a series of tandem mass spectra, to identify correlated pairs of fragment ions produced along the same fragmentation pathway of the same parent (e.g., peptide) ion. Here, we apply 2D-PC-MS to the analysis of intact protein ions in a standard linear ion trap mass analyzer, using the fact that the fragment-fragment correlation signals are much more specific to the biomolecular sequence than one-dimensional (1D) tandem mass spectrometry (MS/MS) signals at the same mass accuracy and resolution. We show that from the distribution of signals on a 2D-PC-MS map it is possible to extract the charge state of both parent and fragment ions without resolving the isotopic envelope. Furthermore, the 2D map of fragment-fragment correlations naturally separates the products of the primary decomposition pathways of the molecular ions from those of the secondary ones. We access this spectral information using an adapted version of the Hough transform. We demonstrate the successful identification of highly charged, intact protein molecules bypassing the need for high mass resolution. Using this technique, we also perform the in silico deconvolution of the overlapping fragment ion signals from two co-isolated and co-fragmented intact proteins, demonstrating a viable new method for the concurrent mass spectrometric identification of a mixture of intact protein ions from the same fragment ion spectrum.

Extracting sub-cycle electronic and nuclear dynamics from high harmonic spectra.

We present a new methodology for measuring few-femtosecond electronic and nuclear dynamics in both atoms and polyatomic molecules using multidimensional high harmonic generation (HHG) spectroscopy measurements, in which the spectra are recorded as a function of the laser intensity to form a two-dimensional data set. The method is applied to xenon atoms and to benzene molecules, the latter exhibiting significant fast nuclear dynamics following ionization. We uncover the signature of the sub-cycle evolution of the returning electron flux in strong-field ionized xenon atoms, implicit in the strong field approximation but not previously observed directly. We furthermore extract the nuclear autocorrelation function in strong field ionized benzene cations, which is determined to have a decay of [Formula: see text] fs, in good agreement with the [Formula: see text] fs obtained from direct dynamics variational multi-configuration Gaussian calculations. Our method requires minimal assumptions about the system, and is applicable even to un-aligned polyatomic molecules.

Electronic Population Transfer via Impulsive Stimulated X-Ray Raman Scattering with Attosecond Soft-X-Ray Pulses.

Free-electron lasers provide a source of x-ray pulses short enough and intense enough to drive nonlinearities in molecular systems. Impulsive interactions driven by these x-ray pulses provide a way to create and probe valence electron motions with high temporal and spatial resolution. Observing these electronic motions is crucial to understand the role of electronic coherence in chemical processes. A simple nonlinear technique for probing electronic motion, impulsive stimulated x-ray Raman scattering (ISXRS), involves a single impulsive interaction to produce a coherent superposition of electronic states. We demonstrate electronic population transfer via ISXRS using broad bandwidth (5.5 eV full width at half maximum) attosecond x-ray pulses produced by the Linac Coherent Light Source. The impulsive excitation is resonantly enhanced by the oxygen 1s→2π^{*} resonance of nitric oxide (NO), and excited state neutral molecules are probed with a time-delayed UV laser pulse.

Attosecond transient absorption spooktroscopy: a ghost imaging approach to ultrafast absorption spectroscopy.

The recent demonstration of isolated attosecond pulses from an X-ray free-electron laser (XFEL) opens the possibility for probing ultrafast electron dynamics at X-ray wavelengths. An established experimental method for probing ultrafast dynamics is X-ray transient absorption spectroscopy, where the X-ray absorption spectrum is measured by scanning the central photon energy and recording the resultant photoproducts. The spectral bandwidth inherent to attosecond pulses is wide compared to the resonant features typically probed, which generally precludes the application of this technique in the attosecond regime. In this paper we propose and demonstrate a new technique to conduct transient absorption spectroscopy with broad bandwidth attosecond pulses with the aid of ghost imaging, recovering sub-bandwidth resolution in photoproduct-based absorption measurements.

Attosecond soft X-ray high harmonic generation.

High harmonic generation (HHG) of an intense laser pulse is a highly nonlinear optical phenomenon that provides the only proven source of tabletop attosecond pulses, and it is the key technology in attosecond science. Recent developments in high-intensity infrared lasers have extended HHG beyond its traditional domain of the XUV spectral range (10-150 eV) into the soft X-ray regime (150 eV to 3 keV), allowing the compactness, stability and sub-femtosecond duration of HHG to be combined with the atomic site specificity and electronic/structural sensitivity of X-ray spectroscopy. HHG in the soft X-ray spectral region has significant differences from HHG in the XUV, which necessitate new approaches to generating and characterizing attosecond pulses. Here, we examine the challenges and opportunities of soft X-ray HHG, and we use simulations to examine the optimal generating conditions for the development of high-flux, attosecond-duration pulses in the soft X-ray spectral range. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Direct characterization of tuneable few-femtosecond dispersive-wave pulses in the deep UV.

Dispersive wave emission (DWE) in gas-filled hollow-core dielectric waveguides is a promising source of tuneable coherent and broadband radiation, but so far the generation of few-femtosecond pulses using this technique has not been demonstrated. Using in-vacuum frequency-resolved optical gating, we directly characterize tuneable 3 fs pulses in the deep ultraviolet generated via DWE. Through numerical simulations, we identify that the use of a pressure gradient in the waveguide is critical for the generation of short pulses.

Apparatus for soft x-ray table-top high harmonic generation.

There has been considerable recent interest in tabletop soft X-ray attosecond sources enabled by the new generation of intense, few-cycle laser sources at operating wavelengths longer than 800 nm. In our recent work [Johnson et al., Sci. Adv. 4(5), eaar3761 (2018)], we have demonstrated a new regime for the generation of X-ray attosecond pulses in the water window (284-540 eV) by high-harmonic generation, which resulted in soft X-ray fluxes of ≈109 photons/s and a maximum photon energy of 600 eV, an order of magnitude and 50 eV higher, respectively, than previously attained with few-cycle drivers. Here we present the key elements of our apparatus for the generation and detection of soft X-ray high harmonic radiation in the water window. Of critical importance is a differentially pumped gas target capable of supporting the multi-atmospheric pressures required to phase-match the high energy emission while strongly constraining the gas density, suppressing the effects of ionization and absorption outside the interaction region.

Low-Energy Electron Emission in the Strong-Field Ionization of Rare Gas Clusters.

Clusters and nanoparticles have been widely investigated to determine how plasmonic near fields influence the strong-field induced energetic electron emission from finite systems. We focus on the contrary, i.e., the slow electrons, and discuss a hitherto unidentified low-energy structure (LES) in the photoemission spectra of rare gas clusters in intense near-infrared laser pulses. For Ar and Kr clusters we find, besides field-driven fast electrons, a robust and nearly isotropic emission of electrons with <4 eV kinetic energies that dominates the total yield. Molecular dynamics simulations reveal a correlated few-body decay process involving quasifree electrons and multiply excited ions in the nonequilibrium nanoplasma that results in a dominant LES feature. Our results indicate that the LES emission occurs after significant nanoplasma expansion, and that it is a generic phenomenon in intense laser nanoparticle interactions, which is likely to influence the formation of highly charged ions.

High-flux soft x-ray harmonic generation from ionization-shaped few-cycle laser pulses.

Laser-driven high-harmonic generation provides the only demonstrated route to generating stable, tabletop attosecond x-ray pulses but has low flux compared to other x-ray technologies. We show that high-harmonic generation can produce higher photon energies and flux by using higher laser intensities than are typical, strongly ionizing the medium and creating plasma that reshapes the driving laser field. We obtain high harmonics capable of supporting attosecond pulses up to photon energies of 600 eV and a photon flux inside the water window (284 to 540 eV) 10 times higher than previous attosecond sources. We demonstrate that operating in this regime is key for attosecond pulse generation in the x-ray range and will become increasingly important as harmonic generation moves to fields that drive even longer wavelengths.

An apparatus for quantitative high-harmonic generation spectroscopy in molecular vapours.

We present an apparatus for performing gas phase high-harmonic generation spectroscopy of molecules primarily found in the liquid phase. Liquid molecular samples are heated in a temperature controlled bath and their vapour is used to back a continuous flow gas jet, with vapour pressures of over 1 bar possible. In order to demonstrate the system, we perform high harmonic spectroscopy experiments in benzene with a 1.8 µm driving field. Using the unique capabilities of the system, we obtain spectra that are nearly free from the effects of longitudinal phase-matching, amenable to comparison with advanced numerical modelling.