Coupling of a Nuclear Transition to a Surface Acoustic Wave
Mechanical modulation of recoilless nuclear transitions allows the dynamic control of $\gamma$-ray emission and absorption. Accessing modulation frequencies well above the nuclear linewidth enables coherent manipulation of the nuclear response. Here we demonstrate high frequency control via efficient coupling a film of enriched $^{57}$Fe to a $97.9~\mathrm{MHz}$ surface acoustic wave, nearly two orders of magnitude higher than the nuclear linewidth. The mechanical drive produces a comb of absorption sidebands in the M\"ossbauer spectrum, reflecting the periodic time modulation of the nuclear transitions. This constitutes the highest frequency mechanically driven M\"ossbauer resonance to date. Our solid-state, monolithic platform establishes a new interface between nuclear transitions and high-frequency acoustics, with applications in $\gamma$-ray quantum optics and precision nuclear spectroscopy.