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'.

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.

Dynamics following excitation with attosecond extreme ultraviolet (XUV) pulses arise from enormous numbers of accessible excited states, complicating the retrieval of state-specific time evolutions. We develop attosecond XUV multidimensional spectroscopy here to separate interfering pathways on a near-infrared (NIR) energy axis, retrieving single state dynamics in argon atoms in a two-dimensional (2D) XUV-NIR spectrum. In this experiment, we measure four-wave mixing signal arising from the interaction of XUV attosecond pulses centered around 15 eV with two few-cycle NIR pulses. The 2D spectrum is created by measuring the emitted XUV signal field spectrum while applying narrowband amplitude and phase modulations to one of the NIR pulses. Application of such a technique to systems of high dimensionality will provide for the observation of state-resolved pure electronic dynamics, in direct analogy to phenomena unraveled by multidimensional spectroscopies at optical frequencies.

The autoionization dynamics of the (²P_1/2)ns/d Rydberg states in krypton are investigated using spatially isolated wave-mixing signals generated with a short train of subfemtosecond extreme ultraviolet (XUV) pulses and noncollinear, few-cycle near infrared pulses. Despite ubiquitous quantum beat oscillations from XUV-induced coherences within the excited-state manifold, these wave-mixing spectra allow for the simultaneous evaluation of autoionization lifetimes from a series of Rydberg states above the first ionization potential. Experimentally measured lifetimes of 22 ± 8 fs, 33 ± 6 fs, and 49 ± 6 fs for the wave-mixing signals emitting from the (²P_1/2)6d/8s, (²P_1/2)7d/9s, and (²P_1/2)8d/10s resonances compare favorably with lifetimes for the (²P_1/2)6d, 7d, and 8d Rydberg states determined from spectral linewidths. Analysis of the quantum beats reveals that the enhancement of wave-mixing pathways that couple the (²P_1/2)nd states to themselves leads to individual reporter state-dependent decays in the wave-mixing signals. The results demonstrate the promise of wave-mixing spectroscopies with subfemtosecond XUV pulses to provide valuable insights into processes governed by electronic dynamics.

Noncollinear wave-mixing spectroscopies with attosecond extreme ultraviolet (XUV) pulses provide unprecedented insight into electronic dynamics. In infrared and visible regimes, heterodyne detection techniques utilize a reference field to amplify wave-mixing signals while simultaneously allowing for phase-sensitive measurements. Here, we implement a self-heterodyned detection scheme in noncollinear wave-mixing measurements with a short attosecond XUV pulse train and two few-cycle near infrared (NIR) pulses. The initial spatiotemporally overlapped XUV and NIR pulses generate a coherence of both odd (1snp) and even (1sns and 1snd) parity states within gaseous helium. A variably delayed noncollinear NIR pulse generates angularly-dependent four-wave mixing signals that report on the evolution of this coherence. The diffuse angular structure of the XUV harmonics underlying these emission signals is used as a reference field for heterodyne detection, leading to cycle oscillations in the transient wave-mixing spectra. With this detection scheme, wave-mixing signals emitting from at least eight distinct light-induced, or dressed, states can be observed, in contrast to only one light induced state identified in a similar homodyne wave-mixing measurement. In conjunction with the self-heterodyned detection scheme, the noncollinear geometry permits the conclusive identification and angular separation of distinct wave-mixing pathways, reducing the complexity of transient spectra. These results demonstrate that the application of heterodyne detection schemes can provide signal amplification and phase-sensitivity, while maintaining the versatility and selectivity of noncollinear attosecond XUV wave-mixing spectroscopies. These techniques will be important tools in the study of ultrafast dynamics within complex chemical systems in the XUV regime.

The removal of electrons located in the core shells of molecules creates transient states that live between a few femtoseconds to attoseconds. Owing to these short lifetimes, time-resolved studies of these states are challenging and complex molecular dynamics driven solely by electronic correlation are difficult to observe. Here, we obtain few-femtosecond core-excited state lifetimes of iodine monochloride by using attosecond transient absorption on iodine 4d^-16p transitions around 55 eV. Core-level ligand field splitting allows direct access of excited states aligned along and perpendicular to the ICl molecular axis. Lifetimes of 3.5 ± 0.4 fs and 4.3 ± 0.4 fs are obtained for core-hole states parallel to the bond and 6.5 ± 0.6 fs and 6.9 ± 0.6 fs for perpendicular states, while nuclear motion is essentially frozen on this timescale. Theory shows that the dramatic decrease of lifetime for core-vacancies parallel to the covalent bond is a manifestation of non-local interactions with the neighboring Cl atom of ICl.

Nonlinear spectroscopies are utilized extensively for selective measurements of chemical dynamics in the optical, infrared, and radio-frequency regimes. The development of these techniques for extreme ultraviolet (XUV) light sources facilitates measurements of electronic dynamics on attosecond timescales. Here, we elucidate the temporal dynamics of nonlinear signal generation by utilizing a transient grating scheme with a subfemtosecond XUV pulse train and two few-cycle near-infrared pulses in atomic helium. Simultaneous detection of multiple diffraction orders reveals delays of ≥1.5 fs in higher-order XUV signal generation, which are reproduced theoretically by solving the coupled Maxwell-Schrödinger equations and with a phase grating model. The delays result in measurable order-dependent differences in the energies of transient light induced states. As nonlinear methods are extended into the attosecond regime, the observed higher-order signal generation delays will significantly impact and aid temporal and spectral measurements of dynamic processes.