X-ray spectroscopy is a powerful technique for studying strongly correlated electronic states, and I study it theoretically. In X-ray spectroscopy, a material is irradiated with high-energy X-rays, which knock electrons out of the inner-shell level and cause them to be emitted as photoelectrons. At this time, positively charged holes in the core level become localized test charges that are instantaneously introduced at atomic positions in the material, inducing a variety of valence electron responses in strongly correlated electron systems. This change is clearly etched in the ensuing X-ray emission spectrum. In other words, the emission spectrum clearly reflects the details of the relaxation dynamics of the electronic states of strongly correlated electron systems. Recent advances in experimental techniques have enabled us to measure the emission spectra with high resolution, and it is necessary to develop advanced theoretical analysis methods to clarify the quantum effects in the relaxation processes from the experimental results.

　In this background, we focus on XEPECS, a spectroscopic method for the coincidence measurement of photoelectron and emitted x-ray photon. This is the only spectroscopy that can select multiple quantum transition paths that interfere with each other in the ultrafast electron relaxation process associated with core-excitation. Although no experiments have been performed yet due to the low signal strength, we will conduct a detailed theoretical study of XEPECS for strongly correlated materials to advance the method ahead of the rest of the world.

　Furthermore, we envision that a new type of quantum entanglement generation is possible by applying XEPECS to strongly correlated materials. In the XEPECS process, photoelectrons and emitted X-ray photons are coincidence emitted from strongly correlated materials due to inner-shell excitation, which is thought to cause quantum entanglement reflecting the electronic state of strongly correlated materials. In this study, we theoretically establish a method to generate and control the correlation between the spin of photoelectrons and the polarization of X-ray photons by XEPECS. This will lead to the proposal of a completely new "quantum entanglement spectroscopy" in the X-ray region, which has never been done before. For this purpose, it is essential to establish a precise theoretical method for XEPECS that takes into account electron correlation effects and electronic relaxation processes specific to solid crystals, which is the "pillar" of this research.