Analysis of the light shift in the hyper-Ramsey scheme of two-level atom interrogation in an optically dense medium

The properties of the Ramsey resonance and its sensitivity to the light shift of the atomic transition frequency are investigated in the case of the hyper-Ramsey interrogation in an optically dense medium of cold atoms. The shape of the interrogating pulses varies significantly due to the processes of absorption and dispersion in the atomic medium, which leads to a distortion of the Ramsey resonance and a periodic change in the central minimum to the maximum and vice versa. The dependence of the position of the central resonance on the light shift of the atomic transition is found with the attenuation of radiation in the medium taken into account. It is shown that in a certain section of the medium this dependence becomes N-shaped.