Quantum Electrodynamics in Strong Electromagnetic Fields: Substate Resolved K$\alpha$ Transition Energies in Helium-like Uranium

Using novel metallic magnetic calorimeter detectors at the CRYRING@ESR, we recorded X-ray spectra of stored and electron cooled helium-like uranium (U$^{90+}$) with an unmatched spectral resolution of close to 90 eV. This allowed for an accurate determination of the energies of all four components of the K$\alpha$ transitions in U$^{90+}$. We find good agreement with state-of-the-art bound-state QED calculations for the strong-field regime. Our results do not support any systematic deviation between experiment and theory in helium-like systems, the presence of which was subject of intense debates in recent years.