To shorten the duration of x-ray pulses, we present a nonlinear optical technique using atoms with core-hole vacancies (core-hole atoms) generated by inner-shell photoionization. The weak Coulomb screening in the core-hole atoms results in decreased absorption at photon energies immediately above the absorption edge. By employing this phenomenon, referred to as saturable absorption, we successfully reduce the duration of x-ray free-electron laser pulses (photon energy: 9.000 keV, duration: 6–7 fs, fluence: $2.0–3.5\times {10}^5\mathrm{J}/{\mathrm{cm}}^2$) by $\sim 35\%$. This finding that core-hole atoms are applicable to nonlinear x-ray optics is an essential stepping stone for extending nonlinear technologies commonplace at optical wavelengths to the hard x-ray region.

• Received 2 March 2021
• Accepted 7 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.163903