Attosecond science opened the door to observing nuclear and electronic dynamics in real time and has begun to expand beyond its traditional grounds. Among several spectroscopic techniques, X-ray transient absorption spectroscopy has become key in understanding matter on ultrafast time scales. In this review, we illustrate the capabilities of this unique tool through a number of iconic experiments. We outline how coherent broadband X-ray radiation, emitted in high-harmonic generation, can be used to follow dynamics in increasingly complex systems. Experiments performed in both molecules and solids are discussed at length, on time scales ranging from attoseconds to picoseconds, and in perturbative or strong-field excitation regimes. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

In Peierls-distorted materials, photoexcitation leads to a strongly coupled transient response between structural and electronic degrees of freedom, always measured independently of each other. Here we use transient reflectivity in the extreme ultraviolet to quantify both responses in photoexcited bismuth in a single measurement. With the help of first-principles calculations based on density-functional theory (DFT) and time-dependent DFT, the real-space atomic motion and the temperature of both electrons and holes as a function of time are captured simultaneously, retrieving an anticorrelation between the A1g phonon dynamics and carrier temperature. The results reveal a coherent, bidirectional energy exchange between carriers and phonons, which is a dynamical counterpart of the static Peierls-Jones distortion, providing validation of previous theoretical predictions.

Attosecond transient absorption spectroscopy (ATAS) is used to observe photoexcited dynamics with outstanding time resolution. The main experimental challenge of this technique is that high-harmonic generation sources show significant instabilities, resulting in sub-par sensitivity when compared to other techniques. This paper proposes edge-pixel referencing as a means to suppress this noise. Two approaches are introduced: the first is deterministic and uses a correlation analysis, while the second relies on singular value decomposition. Each method is demonstrated and quantified on a noisy measurement taken on WS₂ and results in a fivefold increase in sensitivity. The combination of the two methods ensures the fidelity of the procedure and can be implemented on live data collection but also on existing datasets. The results show that edge-referencing methods bring the sensitivity of ATAS near the detector noise floor. An implementation of the post-processing code is provided to the reader.

Few-femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy, performed with optical 500-1000 nm supercontinuum and broadband XUV pulses (30-50 eV), simultaneously probes dynamics of photoexcited carriers in WS$_{2}$ at the W O$_3$ edge (37-45 eV) and carrier-induced modifications of core-exciton absorption at the W N$_{6,7}$ edge (32-37 eV). Access to continuous core-to-conduction band absorption features and discrete core-exciton transitions in the same XUV spectral region in a semiconductor provides a novel means to investigate the effect of carrier excitation on core-exciton dynamics. The core-level transient absorption spectra, measured with either pulse arriving first to explore both core-level and valence carrier dynamics, reveal that core-exciton transitions are strongly influenced by the photoexcited carriers. A $1.2\pm0.3$ ps hole-phonon relaxation time and a $3.1\pm0.4$ ps carrier recombination time are extracted from the XUV transient absorption spectra from the core-to-conduction band transitions at the W O$_{3}$ edge. Global fitting of the transient absorption signal at the W N$_{6,7}$ edge yields $\sim 10$ fs coherence lifetimes of core-exciton states and reveals that the photoexcited carriers, which alter the electronic screening and band filling, are the dominant contributor to the spectral modifications of core-excitons and direct field-induced changes play a minor role. This work provides a first look at the modulations of core-exciton states by photoexcited carriers and advances our understanding of carrier dynamics in metal dichalcogenides.

Few-femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy, performed with optical 500-1000-nm supercontinuum and broadband XUV pulses (30-50 eV), simultaneously probes dynamics of photoexcited carriers in WS2 at the W O3 edge (37-45 eV) and carrier-induced modifications of core-exciton absorption at the WN6,7 edge (32-37 eV). Access to continuous core-to-conduction-band absorption features and discrete core-exciton transitions in the same XUV spectral region in a semiconductor provides a means to investigate the effect of carrier excitation on core-exciton dynamics. The core-level transient absorption spectra, measured with either pulse arriving first to explore both core-level and valence carrier dynamics, reveal that core-exciton transitions are strongly influenced by the photoexcited carriers. A 1.2±0.3 ps hole-phonon relaxation time and a 3.1±0.4 ps carrier recombination time are extracted from the XUV transient absorption spectra from the core-to-conduction-band transitions at the W O3 edge. Global fitting of the transient absorption signal at the W N6,7 edge yields ∼10 fs coherence lifetimes of core-exciton states and reveals that the photoexcited carriers, which alter the electronic screening and band filling, are the dominant contributor to the spectral modifications of core excitons and direct field-induced changes play a minor role. This work provides a first look at the modulations of core-exciton states by photoexcited carriers and advances our understanding of carrier dynamics in metal dichalcogenides.

We developed and implemented an experimental setup for the generation of high-energy high-order harmonics in argon gas for nonlinear experiments in the extreme ultraviolet (XUV) spectral range. High-order harmonics were generated by loosely focusing a high-energy laser pulse centered around 800 nm into a gas cell filled with argon in a phase-matching condition. The wavefront distortions of the driving pulse were corrected by a deformable mirror, and the XUV conversion efficiency was significantly improved due to the excellent beam profile at focus. A high-damage-threshold beam splitter was used to eliminate high-energy driving pulses co-propagating with high-order harmonics. The setup has a potential to provide intense ultrashort XUV pulses reaching the intensity levels required for nonlinear experiments in the XUV spectral range.

It has been demonstrated in the past that high fluxes of extreme ultraviolet (XUV) light could be obtained by driving high harmonic generation (HHG) with high energy lasers. However, the peak intensity at the focal point of a femtosecond laser with more than 100 mJ can be too high for phase-matched HHG in gases. We propose a method to optimize the spatial profile at off-focus locations of the high energy driving laser to avoid fully ionizing the target atoms. The beam profile before or after the focal point depends on the wavefront quality of the laser beam and the near field intensity distribution. The beam spot diameter reaches three times that at the focus by adding customized wavefront terms. An XUV pulse energy of 5.6 μJ was obtained from HHG when a larger off-focus spot of a 500 mJ Ti: sapphire laser beam was applied in an argon gas cell.

Extremely nonlinear spectroscopy based on high-order-harmonic generation has become a powerful investigation method for attosecond dynamics in gas and solid targets. In particular, the phase of harmonic emission was shown to carry profound insight into atomic and molecular structure and dynamics. However, current techniques offer phase measurements only along specific directions, thus providing partial characterization. Here we report on a new approach combining optical and quantum interferometers measuring along two dimensions the intensity and phase of harmonic emission from aligned molecules in the exact same experimental conditions. This two-dimensional cartography technique measures the phase with no arbitrary offset and no uncertainty on its sign. Measurements along different dimensions can be combined in two ways: either a single mapping or a redundant mapping allowing high-precision phase recovery using a Shack–Hartmann-like algorithm. We demonstrate both methods in a nitrogen test case, which allows disentangling structural and dynamical effects. Two-dimensional phase cartography paves the way to high-resolution high-harmonic spectroscopy for applications such as quantum orbital tomography and attosecond charge migration in molecules.

Excitation of ionic solids with extreme ultraviolet pulses creates localized core-level excitons, which in some cases couple strongly to the lattice. Here, core-level-exciton states of magnesium oxide are studied in the time domain at the Mg L_{2,3} edge with attosecond transient reflectivity spectroscopy. Attosecond pulses trigger the excitation of these short-lived quasiparticles, whose decay is perturbed by time-delayed near-infrared pulses. Combined with a few-state theoretical model, this reveals that the infrared pulse shifts the energy of bright (dipole-allowed) core-level-exciton states as well as induces features arising from dark core-level excitons. We report coherence lifetimes for the two lowest core-level excitons of 2.3±0.2 and 1.6±0.5  fs and show that these are primarily a consequence of strong exciton-phonon coupling, disclosing the drastic influence of structural effects in this ultrafast relaxation process.

Strong enhancement of exciton binding has been observed in valence-excitons in the optical regime of 2D materials. We report direct observation of long-lived core-exciton states in transition metal dichalcogenides by attosecond transient absorption spectroscopy in the XUV.