We report clear experimental evidence for second harmonic generation at hard x-ray wavelengths. Using a 1.7 Å pumping beam generated by a free electron laser, we observe second harmonic generation in diamond. The generated second harmonic is of order 10 times the background radiation, scales quadratically with pump pulse energy, and is generated over a narrow phase-matching condition. Of importance for future experiments, our results indicate that it is possible to observe nonlinear x-ray processes in crystals at pump intensities exceeding ${10}^{16}\mathrm{W}/{\mathrm{cm}}^2$.

We describe an experiment demonstrating ghost imaging with an incoherent low brightness X-ray tube source. We reconstruct the images of 10 μm and 100 μm slits with very high contrast. Our results advance the possibilities that the high-resolution method of ghost diffraction will be utilized with tabletop X-ray sources.

We demonstrate computational ghost imaging at X-ray wavelengths with only one single-pixel detector. We show that, by using a known designed mask as a diffuser that induces intensity fluctuations in the probe beam, it is possible to compute the propagation of the electromagnetic field in the absence of the investigated object. We correlate these calculations with the measured data when the object is present in order to reconstruct the images of 50 μm and 80 μm slits. Our results open the possibilities for X-ray high-resolution imaging with partially coherent X-ray sources and can lead to a powerful tool for X-ray three-dimensional imaging.

We report the experimental observation of ghost imaging with paired x-ray photons, which are generated by parametric downconversion. We use the one-to-one relation between the photon energies and the emission angles and the anticorrelation between the $k$-vectors of the signal and the idler photons to reconstruct the images of slits with nominally zero background levels. Further extension of our procedure can be used for the observation of various quantum phenomena at x-ray wavelengths.

Chemical element mapping is an imaging tool that provides essential information about composite materials, and it is crucial for a broad range of fields ranging from fundamental science to numerous applications. Methods that exploit x-ray fluorescence are very advantageous and are widely used, but require focusing of the input beam and raster scanning of the sample. Thus, the methods are slow and exhibit limited resolution due to focusing challenges. Here, we demonstrate an x-ray fluorescence method based on computational ghost imaging that overcomes those limitations since it does not require focusing and show that when it is combined with compressed sensing the total measurement time can be significantly reduced. Our method opens the possibility to significantly enhance the resolution of chemical element maps and to extend the applicability of x-ray fluorescence inspection to new fields where the measurement time is a critical parameter.

We report the observation of parametrically down-converted x-ray signal photons at photon energies that correspond to idler photons at optical wavelengths. The count-rate dependence on the angles of the input beam and of the detector and on the slit sizes agrees with theory within the experimental uncertainties. The nonlinear susceptibility, which we calculated from the measured efficiencies, is comparable to the nonlinear susceptibility evaluated from the measurements of x-ray and optical wave mixing. The results of the present Letter advance the development of a spectroscopy method for probing valence-electron charges and the microscopic optical response of crystals with atomic-scale resolution.