  To shorten the x-ray pulse duration, we present a nonlinear optical technique
using core-hole atoms generated by x-ray irradiation on matter. The weak
Coulomb screening in the core-hole atoms results in deterioration of absorption
properties for the photon energy 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\times10^5 J/cm^2) by \~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 x-ray region.
