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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, the resulting inner-shell X-ray laser pulses can exhibit strong spatial inhomogeneities as well as spectral inhomogeneities and broadening. Through 3D Maxwell Bloch theory we show that the observed spatial inhomogeneities result from X-ray filamentation, and that the spectral broadening is driven by Rabi cycling with sub-femtosecond periods. These findings indicate that we have generated Angstrom-wavelength x-ray pulses (containing ${10^{6}}$ - ${10^{8}}$ photons) in the strong lasing regime, some of them with pulse lengths of less than 100 attoseconds.

Coherent nonlinear spectroscopies and imaging in the X-ray domain provide direct insight into the coupled motions of electrons and nuclei with resolution on the electronic length and time scale. The experimental realization of such techniques will strongly benefit from access to intense, coherent pairs of femtosecond X-ray pulses. We have observed phase-stable X-ray pulse pairs containing more thank 3 x 10e7 photons at 5.9 keV (2.1 Angstrom) with about 1 fs duration and 2-5 fs separation. The highly directional pulse pairs are manifested by interference fringes in the superfluorescent and seeded stimulated manganese K-alpha emission induced by an X-ray free-electron laser. The fringes constitute the time-frequency X-ray analogue of the Young double-slit interference allowing for frequency-domain X-ray measurements with attosecond time resolution., Comment: 39 pages, 13 figures, to be published

Photosynthesis powers life on our planet. The basic photosynthetic architecture comprises antenna complexes to harvest solar energy and reaction centers to convert the energy into a stable charge separated state. In oxygenic photosynthesis, the initial charge separation event occurs in the photosystem II reaction center; the only known natural enzyme that uses solar energy to split water. Energy transfer and charge separation in photosynthesis are rapid and have high quantum efficiencies. Recently, nonlinear spectroscopic experiments have suggested that electronic coherence may play a role in energy transfer efficiency in antenna complexes. Here we report the observation of coherence in the photosystem II reaction center by two dimensional electronic spectroscopy. The frequencies of the observed coherences match exciton difference frequencies and/or known vibrational modes of the photosystem II reaction center. These observations raise questions about the possible role of electronic and/or vibrational coherence in the fundamental charge separation process in oxygenic photosynthesis., Comment: 31 pages, 5 figures and supplementary information