Attosecond Inner-Shell Lasing at Angstrom Wavelengths

Since the invention of the laser nonlinear effects such as filamentation, Rabi-cycling and collective emission have been explored in the optical regime leading to a wide range of scientific and industrial applications. X-ray free electron lasers (XFELs) have led to the extension of many optical techniques to X-rays for their advantages of angstrom scale spatial resolution and elemental specificity. One such example is XFEL driven population inversion of 1s core hole states resulting in inner-shell K${\alpha}$ (2p to 1s) X-ray lasing in elements ranging from neon to copper, which has been utilized for nonlinear spectroscopy and development of next generation X-ray laser sources. Here we show that strong lasing effects, similar to those observed in the optical regime, can occur at 1.5 to 2.1 angstrom wavelengths during high intensity (> ${10^{19}}$ W/cm${^{2}}$) XFEL driven inner-shell lasing and superfluorescence of copper and manganese. Depending on the temporal substructure of the XFEL pump pulses(containing ${~10^{6}}$ - ${10^{8}}$ photons) i, the resulting inner-shell X-ray laser pulses can exhibit strong spatial inhomogeneities as well as spectral splitting, inhomogeneities and broadening. Through 3D Maxwell Bloch theory we show that the observed spatial inhomogeneities result from X-ray filamentation, and that the spectral splitting and broadening is driven by Rabi cycling with sub-femtosecond periods. Our simulations indicate that these X-ray pulses can have pulse lengths of less than 100 attoseconds and coherence properties that open the door for quantum X-ray optics applications.