Theoretical description of attosecond x-ray imaging and spectroscopy of electron dynamics

We explore how attosecond x-ray and extreme ultraviolet pulses can be employed for imaging electron dynamics in real time. In the first part of my talk, I will review our theoretical developments to describe pump-probe experiments. We describe ultrafast imaging by means of photoelectron momentum microscopy with extreme ultraviolet pulses. I will talk about attosecond momentum-resolved resonant x-ray scattering that is another imaging technique to follow electron dynamics in materials. We develop an ab initio scheme based on the Bethe-Salpeter equation and the full-potential linearized augmented-plane-wave method to treat optical-pump -- resonant x-ray probe-techniques and will demonstrate our results for x-ray absorption spectroscopy of optically excited excitons in 4H-SiC. In the second part of my talk, I will present our ab initio description of experiments involving wave mixing of optical and x-ray pulses, namely, attosecond x-ray diffraction and absorption spectroscopy from materials during the time they are optically driven by light.