Addition to the dynamic Stark shift of the coherent population trapping resonance

This paper presents a theoretical study of the light-induced shift of the coherent population trapping resonance. An analytical model is proposed that describes the interaction of two radiation components with an atomic system using a $Λ$ scheme and takes into account an additional level of excited state. Both weak and strong coupling regimes with off-resonant transitions are considered. It is shown that, in addition to the conventional dynamic Stark shift, an extra shift arises due to the distortion of the resonance line shape when bichromatic laser radiation interacts with off-resonant atomic transitions. An analytical expression for this additional shift is derived in the weak-coupling limit, and its significant impact on the resonance shape and sensitivity to the intensities of the laser field components is demonstrated. It is found that under strong coupling conditions, the additional shift can deviate substantially from a linear dependence on light intensity, suggesting new opportunities for controlling light shifts in precision atomic devices such as quantum frequency standards.