Attosecond inner-shell lasing at ångström wavelengths

Since the invention of the laser, nonlinear effects such as filamentation¹, Rabi cycling^2,3 and collective emission⁴ have been explored in the optical regime, leading to a wide range of scientific and industrial applications^5-8. X-ray free-electron lasers (XFELs) have extended many optical techniques to X-rays for their advantages of ångström-scale spatial resolution and elemental specificity⁹. An example is XFEL-driven inner-shell Kα₁ (2p_3/2 → 1s_1/2) X-ray lasing in elements ranging from neon to copper, which has been used for nonlinear spectroscopy and development of new X-ray laser sources^10-16. Here we show that strong lasing effects similar to those in the optical regime can occur at 1.5-2.1 Å wavelengths during high-intensity (>10¹⁹ W cm^-2) XFEL-driven Kα₁ lasing of copper and manganese. Depending on the temporal XFEL pump pulse substructure, the resulting X-ray pulses (about 10⁶-10⁸ photons) can exhibit strong spatial inhomogeneities and spectral splitting, inhomogeneities and broadening. Three-dimensional Maxwell-Bloch calculations¹⁷ show that the observed spatial inhomogeneities result from X-ray filamentation and that the broad spectral features are driven by sub-femtosecond Rabi cycling. Our simulations indicate that these X-ray pulses can have pulse lengths of less than 100 attoseconds and coherence properties that provide opportunities for quantum X-ray optics applications.