Determining X-Ray Nonlinear Susceptibility of Diamond by the Optical Fano Effect

X-ray nonlinear optics, which has been considered as a scientific frontier to be explored with x-ray free-electron lasers, is accessible with existing synchrotron x-ray sources, revealing its unique features. We demonstrate that x-ray parametric down-conversion is observed indirectly through quantum mechanical interference known as the Fano effect. By introducing a novel concept of photonic discrete levels, we determine the second order nonlinear susceptibility of diamond, and find a strong resonance enhancement at the core absorption edge that presents firm experimental evidence to develop x-ray nonlinear optics.