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.

We describe high energy-resolution measurements of parametric down-conversion of x-rays into ultraviolet radiation using a standard laboratory x-ray tube source with very minor modifications. We measure the effect in diamond and in lithium fluoride crystals in the ultraviolet range from 30 eV to 65 eV. We show that the effect depends strongly on the fluorine LI edge at 37 eV and on the K edge of the lithium at 55 eV. The comparison with theory reveals that the classical model that was previously used for the description of the effect agrees with the experimental results in diamond. However, the discrepancies of the model with the experimental results in lithium fluoride are prominent.

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We present the observation of peculiar non-monotonic photon energy dependencies of the count rates and of the rocking curves of parametric down-conversion of x rays into ultraviolet far from any atomic resonances. The observations cannot be explained by models that consider only atomic or bond charge responses and suggest that collective phenomena contribute to the effect. We propose an interpretation that includes nonlinear interactions with plasmons, which can explain the existence of peaks in this energy range. Our work implies that nonlinear interactions between x rays and either ultraviolet or visible radiation can be utilized as a powerful atomic scale probe for collective effects in solids.