On-demand reconstruction of the waveform of a Mössbauer gamma-ray photon by means of delayed acoustically induced transparency

A method has been proposed to reconstruct at arbitrary time the spectral–temporal characteristics of a 14.4-keV single-photon wave packet that is emitted by a $^{57}$Co source and is resonantly absorbed in the medium of $^{57}$Fe nuclei. The method is based on the frequency separation of the field emitted by the source and resonance nuclear polarization induced by this field by means of delayed acoustically induced transparency of the absorber, which appears after the activation of oscillations of the absorber at the corresponding frequency and amplitude. The proposed method has been compared to the known quantum-optical memory methods and methods of nuclear polarization control in the gamma-ray range. Experimental conditions have been proposed to implement the method. It has been shown that this method allows the implementation of the time-resolved Mössbauer spectroscopy of various media.