Towards novel probes for valence charges via X-ray optical wave mixing

We present a combined theoretical and experimental study of X-ray optical wave mixing. This class of nonlinear phenomena combines the strengths of spectroscopic techniques from the optical domain, with the high-resolution capabilities of X-rays. In particular, the spectroscopic sensitivity of these phenomena can be exploited to selectively probe valence dynamics. Specifically, we focus on the effect of X-ray parametric down-conversion. We present a theoretical description of the process, from which we deduce the observable nonlinear response of valence charges. Subsequently, we simulate scattering patterns for realistic conditions and identify characteristic signatures of the nonlinear conversion. For the observation of this signature, we present a dedicated experimental setup and results of a detailed investigation. However, we do not find evidence of the nonlinear effect. This finding stands in strong contradiction to previous claims of proof-of-principle demonstrations. Nevertheless, we are optimistic to employ related X-ray optical wave mixing processes on the basis of the methods presented here for probing valence dynamics in the future.