Cavity Controls Core-to-Core Resonant Inelastic X-Ray Scattering

X-ray cavity quantum optics with inner-shell transitions has been limited by the spectral overlap between resonant and continuum states. Here, we report the first experimental demonstration of cavity-controlled core-to-core resonant inelastic x-ray scattering (RIXS). We suppress the absorption-edge effects by monitoring the RIXS profile, thereby resolving the resonant state from the overlapping continuum. We observe distinct cavity-induced energy shifts and cavity-enhanced decay rates in the 2⁢𝑝⁢3⁢𝑑RIXS spectra of WSi$_2$. These effects, manifesting as stretched or shifted profiles in the RIXS planes, enable novel spectroscopic applications via cavity-controlled core-hole states. Our results establish core-to-core RIXS as a powerful tool to manipulate inner-shell dynamics in x-ray cavities, offering new avenues for integrating quantum optical effects with x-ray spectroscopy.