Ångstrom and attosecond are the fundamental spatiotemporal scales for electron dynamics in various materials. Although attosecond pulses with wavelengths comparable to the atomic scales are expected to be a key tool in advancing attosecond science, producing high-power hard X-ray attosecond pulses at ångstrom wavelengths remains a formidable challenge. Here, we report the generation of terawatt-scale attosecond hard X-ray pulses using a free-electron laser in a special operation mode. We achieved 9 keV single-spike X-ray pulses with a mean pulse energy of around 180 μJ, exceeding previous reports by more than an order of magnitude, and an estimated average pulse duration of 200 as at full-width at half-maximum. Exploiting the unique capability of the European XFEL, which can deliver ten pulse trains per second with each containing hundreds of pulses at megahertz repetition rates, this study demonstrates the generation of attosecond X-ray pulses at a 2.25 MHz repetition rate. These intense high-repetition-rate attosecond X-ray pulses present transformative prospects for structural and electronic damage-free X-ray measurements and attosecond time-resolved X-ray methodologies, heralding a new era in ultrafast X-ray science.

We theoretically show that a single free electron in circular motion radiates an electromagnetic wave possessing helical phase structure, which is closely related to orbital angular momentum carried by it. We experimentally demonstrate it by interference and double-slit diffraction experiments on radiation from relativistic electrons in spiral motion. Our results indicate that photons carrying orbital angular momentum should be created naturally by cyclotron/synchrotron radiations or Compton scatterings in various situations in cosmic space. We propose promising laboratory vortex photon sources in various wavelengths ranging from radio wave to gamma-rays.

Extreme-ultraviolet vortices may be exploited to steer the magnetic properties of nanoparticles, increase the resolution in microscopy, and gain insight into local symmetry and chirality of a material; they might even be used to increase the bandwidth in long-distance space communications. However, in contrast to the generation of vortex beams in the infrared and visible spectral regions, production of intense, extreme-ultraviolet and x-ray optical vortices still remains a challenge. Here, we present an in-situ and an ex-situ technique for generating intense, femtosecond, coherent optical vortices at a free-electron laser in the extreme ultraviolet. The first method takes advantage of nonlinear harmonic generation in a helical undulator, producing vortex beams at the second harmonic without the need for additional optical elements, while the latter one relies on the use of a spiral zone plate to generate a focused, micron-size optical vortex with a peak intensity approaching ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, paving the way to nonlinear optical experiments with vortex beams at short wavelengths.

The recent development of ultrafast extreme ultraviolet (XUV) coherent light sources bears great potential for a better understanding of the structure and dynamics of matter. Promising routes are advanced coherent control and nonlinear spectroscopy schemes in the XUV energy range, yielding unprecedented spatial and temporal resolution. However, their implementation has been hampered by the experimental challenge of generating XUV pulse sequences with precisely controlled timing and phase properties. In particular, direct control and manipulation of the phase of individual pulses within an XUV pulse sequence opens exciting possibilities for coherent control and multidimensional spectroscopy, but has not been accomplished. Here, we overcome these constraints in a highly time-stabilized and phase-modulated XUV-pump, XUV-probe experiment, which directly probes the evolution and dephasing of an inner subshell electronic coherence. This approach, avoiding any XUV optics for direct pulse manipulation, opens up extensive applications of advanced nonlinear optics and spectroscopy at XUV wavelengths.