Theory and implementation of nonlinear X-ray spectroscopies: application to time-resolved diffraction, X-ray chirality and transient grating experiments

Thanks to the progresses of X-ray light sources, ultrafast non-linear X-ray experiments are now feasible. We discuss how such spectroscopies can be theoretically described in terms of the minimal coupling Hamiltonian, allowing a unified description of diffraction-detected and resonant techniques. Coherent X-ray sources can access new material quantities such as transition charge densities thanks to their atomic resolution. We present how X-ray experiments can make use of their element selectivity to probe matter chirality with additional structural information. Finally, we present hybrid visible pump - X-ray probe transient grating measurements conducted on Bi4Ge3O12 (BGO). This 3rd order technique allows to probe excited carrier dynamics and propagation at unprecedented time and length scale.