Slowing down x-ray photons in a vibrating recoilless resonant absorber

Recently, an observation of acoustically induced transparency (AIT) of a stainless-steel foil for resonant 14.4-keV photons from a radioactive ⁵⁷Co Mössbauer source due to collective uniform oscillations of atomic nuclei was reported [Phys Rev Lett 124,163602, 2020]. In this paper, we propose to use the steep resonant dispersion of the absorber within the AIT spectral window to dramatically reduce a propagation velocity of γ-ray and x-ray photons. In particular, we show that a significant fraction (more than 40%) of a 97-ns γ-ray single-photon wave packet from a ⁵⁷Co radioactive source can be slowed down up to 3 m/s and delayed by 144 ns in a ⁵⁷Fe-enriched stainless-steel foil at room temperature. We also show that a similarly significant slowing down up to 24 m/s and a delay by 42 ns can be achieved for more than 70% of the 100-ns 14.4-keV x-ray single-photon pulse from a synchrotron Mössbauer source available at European Synchrotron Radiation Facility (ESRF) and Spring-8 facility. The propagation velocity can be widely controlled by changing the absorber vibration frequency. Achieving the propagation velocity on the order of 1-50 m/s would set a record in the hard x-ray range, comparable to what was obtained in the optical range.