Attosecond Inner-Shell Lasing at Angstrom Wavelengths

Strong lasing effects, such as Rabi flopping and filamentation, have been explored and applied in the optical regime since the invention of the laser. X-ray free-electron lasers (XFEL) have led to extending nonlinear techniques developed with optical lasers to X-rays as they offer advantages of atomic spatial resolution and element sensitivity. Here we demonstrate that during stimulated emission of the inner-shell 2p-1s transition (Kα) in Cu and Mn, pumped with a very intense XFEL pulse (>10¹⁹ W/cm²), the emitted x-ray signal can behave like a self-focusing filamenting laser pulse with large spectral broadening and inhomogeneities in both the spectral and spatial distribution. Our simulations show that the observed spectral broadening is driven by Rabi flopping with sub-femtosecond periods, and that the spatial distribution arises from gain-guiding driven focusing and filamentation. These findings demonstrate strong lasing physics in the hard x-ray regime, with the generation of attosecond hard X-ray pulses.