Hybridized states of extreme ultraviolet light and matter revealed by nonlinear x-ray scattering

Nonlinear frequency conversion processes are broadly explored and applied in the visible spectral region. Extending these effects into the x-ray spectral domain is challenging due to their inherently low cross section [1]. Yet, these processes are accessible at high-brilliance storage-ring based x-ray sources and x-ray free electron lasers. The process of x-ray parametric down conversion (XPDC) of x-ray photons in a pair of x-ray (signal) and visible (idler) photons is predominantly mediated by the valence electron density and provides a valence sensitive probe of electronic structure. Recently, we developed a quantitative theory [1,3] that linked the measured nonlinear scattering signal to an electronic current-density density correlation function. We identified a characteristic signature, that allows for an unequivocal experimental identification of this extremely weak process – the XPDC emission cone [1]. In a recent experiment, we successfully measured the XPDC cone resulting of nonlinear x-ray scattering of photons of 10 keV from diamond, for idler energies in the range of 100 eV. The XPDC scattering cone clearly shows the contribution of two distinct branches, manifested by a positive and negative signal with respect to the Compton scattering background. We interpret this finding as inelastic x-ray scattering from a XUV polaritonic excitation in diamond. A simple polariton model of two coupled electronic and photonic excited states concurrent with energy and momentum conservation of the nonlinear scattering process agrees with the data and corroborates our interpretation. Momentum-resolved nonlinear x-ray scattering thus provides a means to determine the microscopic structure of EUV polaritons on the length scale of the x-ray wavelength.



[1] C. Boemer, D. Krebs, A. Benediktovitch, E. Rossi, S. Huotari & N. Rohringer, Faraday Discuss. 228, 451 (2021).

[3] D. Krebs and N. Rohringer, Phys. Rev. X (under review), arXiv:2104.05838