Attosecond-pump/attosecond-probe experiments have long been sought as the most straightforward method for observing electron dynamics in real time. Although there has been much success with overlapped near-infrared femtosecond and extreme ultraviolet attosecond pulses combined with theory, true attosecond-pump/attosecond-probe experiments have been limited. We used a synchronized attosecond x-ray pulse pair from an x-ray free-electron laser to study the electronic response to valence ionization in liquid water through all x-ray attosecond transient absorption spectroscopy (AX-ATAS). Our analysis showed that the AX-ATAS response is confined to the subfemtosecond timescale, eliminating any hydrogen atom motion and demonstrating experimentally that the 1b₁splitting in the x-ray emission spectrum is related to dynamics and is not evidence of two structural motifs in ambient liquid water.

High-intensity ultrashort X-ray free-electron laser (XFEL) pulses are revolutionizing the study of fundamental nonlinear x-ray matter interactions and coupled electronic and nuclear dynamics. To fully exploit the potential of this powerful tool for advanced x-ray spectroscopies, a noninvasive spectral characterization of incident stochastic XFEL pulses with high resolution is a key requirement. Here we present a methodology that combines high-acceptance angle-resolved photoelectron time-of-flight spectroscopy and ghost imaging to enhance the quality of spectral characterization of x-ray free-electron laser pulses. Implementation of this noninvasive high-resolution x-ray diagnostic can greatly benefit the ultrafast x-ray spectroscopy community by functioning as a transparent beamsplitter for applications such as transient absorption spectroscopy in averaging mode as well as covariance-based x-ray nonlinear spectroscopies in single-shot mode where the shot-to-shot fluctuations inherent to a self-amplified spontaneous emission (SASE) XFEL pulse are a powerful asset.

Propagation of intense X-ray pulses through dense media has led to the observation of phenomena such as atomic X-ray lasing^1,2, self-induced transparency³ and stimulated X-ray Raman scattering (SXRS)⁴. SXRS has been long predicted as a means to launch and probe valence-electron wavepackets and as a building block for nonlinear X-ray spectroscopies^5,6. However, experimental observations of SXRS to date^4,7,8 have not provided spectroscopic information, and theoretical modelling has largely implemented hard-to-realize phase-coherent attosecond pulses. Here we demonstrate SXRS with spectroscopic precision, that is, detection of valence-excited states in neon with a near Fourier-limited joint energy–time resolution of 0.1 eV–40 fs. We used a new covariance analysis between statistically spiky broadband incident X-ray and scattered X-ray Raman pulses. Using 18,000 single shots, we beat not only the incident (about 8 eV) bandwidth but also the approximately 0.2 eV instrumental energy resolution, thus creating super-resolution conditions, in analogy to super-resolved fluorescence microscopy⁹. Our experimental results, supported by ab initio propagation simulations, reveal the competition between lasing in the ion and stimulated Raman scattering in the neutral. We demonstrate enhanced signal collection efficiency and a broad excitation window, surpassing spontaneous Raman efficiencies by orders of magnitude. This stochastic SXRS approach represents a first step towards tracking elementary events that determine chemical outcomes¹⁰.

We present a theoretical study of temporal, spectral, and spatial reshaping of intense, ultrafast x-ray pulses propagating through a resonant medium. Our calculations are based on the solution of a three-dimensional time-dependent Schrödinger-Maxwell equation, with the incident x-ray photon energy on resonance with the core-level $1s\text{−}3p$ transition in neon. We study the evolution of the combined incident and medium-generated field, including the effects of stimulated emission, absorption, ionization, and Auger decay, as a function of the input pulse energy and duration. We find that stimulated Raman scattering between core-excited states $1s^{-1}3p$ and $2p^{-1}3p$ occurs at high x-ray intensity, and that the emission around this frequency is strongly enhanced when also including the similar $1s^{-1}\text{−}2p^{-1}$ response of the ion. We also explore the dependence of x-ray self-induced transparency (SIT) and self-focusing on the pulse intensity and duration, and we find that the stimulated Raman scattering plays an important role in both effects. Finally, we discuss how these nonlinear effects may potentially be exploited as control parameters for pulse properties of x-ray free-electron laser sources.

The sound field due to an arbitrarily oriented quadrupole above an impedance ground is investigated. To simplify the analysis, the atmospheric and topographical effects on sound propagation are ignored. Two different methods are developed to calculate the sound field. First, an asymptotic method is used to derive a close-form analytic solution. Second, a fast field program (quad-FFP) has been developed for numerical computations of the sound field. It is found that numerical results from both methods agree well. In a recent development, it has been shown that the analytic solution of the sound field due to an arbitrarily oriented dipole can be written in the classical form similar to that due to a monopole. However, it is not possible to write the solution in such a form for the case of an arbitrarily oriented quadrupole, but rather the total sound pressure is augmented by two extra terms which are particularly important at a small separation between the source and receiver.