Collective dynamics of nuclei from quadrupole splitting in an x-ray cavity

Mössbauer nuclei with quadrupole-split levels provide a versatile platform for exploring coherent x-ray light-matter interactions. We theoretically study ensembles of ⁵⁷Fe nuclei embedded in thin-film x-ray cavities, explicitly accounting for different orientations of the electric field gradient. By mapping isotropic electric field gradient distributions to an effective equal-weight two-transition model, we derive analytical expressions for the time-dependent reflectivity and reveal the emergence of cavity-mediated quantum beats. The oscillation frequency and temporal profile of these beats can be tuned via the cavity-induced coherent coupling, offering a flexible approach to control collective nuclear dynamics and manipulate nuclear coherence in the x-ray regime.