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The extension of nonlinear spectroscopic techniques into the x-ray domain is in its infancy but holds the promise to provide unique insight into the dynamics of charges in photoexcited processes, which are of fundamental as well as applied interest. We report on the observation of a third order nonlinear process in lithium fluoride at a free-electron laser. Exploring the yield of four wave mixing (FWM) in resonance with transitions to strongly localized core exciton states vs. delocalized Bloch states, we find resonant FWM to be a sensitive probe for the degree of charge localization: substantial sum- and difference-frequency generation is observed exclusively when in a one- or three-photon resonance with a LiF core exciton, with a dipole forbidden transition affecting details of the nonlinear response. Our reflection-geometry-based approach to detect FWM signals enables the study of a wide variety of condensed matter sample systems, provides atomic selectivity via resonant transitions and can be easily scaled to shorter wavelengths at free electron x-ray lasers., Comment: 5 figures, supplement

The Free-Electron Laser (FEL) FLASH offers the worldwide still unique capability to study ultrafast processes with high-flux, high-repetition rate XUV and soft X-ray pulses. The vast majority of experiments at FLASH are of pump-probe type. Many of them rely on optical ultrafast lasers. Here, a novel FEL facility laser is reported which combines high average power output from Yb:YAG amplifiers with spectral broadening in a Herriott-type multi-pass cell and subsequent pulse compression to sub-100 fs durations. Compared to other facility lasers employing optical parametric amplification, the new system comes with significantly improved noise figures, compactness, simplicity and power efficiency. Like FLASH, the optical laser operates with 10 Hz burst repetition rate. The bursts consist of 800 $\mu$s long trains of up to 800 ultrashort pulses being synchronized to the FEL with femtosecond precision. In the experimental chamber, pulses with up to 50 $\mu$J energy, 60 fs FWHM duration and 1 MHz rate at 1.03 $\mu$m wavelength are available and can be adjusted by computer-control. Moreover, nonlinear polarization rotation is implemented to improve laser pulse contrast. First cross-correlation measurements with the FEL at the plane-grating monochromator photon beamline are demonstrated, exhibiting the suitability of the laser for user experiments at FLASH., Comment: 28 pages, 13 figures