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The analytic derivation of the dynamic Stark shift of hydrogenic energylevels in the presence of the circularly polarized laser light is presented. Weuse the classical framework with considering an adiabatically damped laser+atominteraction and an approach relies on time-independent perturbation theory witha second-quantized laser+atom dipole interaction Hamiltonian. We thusinvestigate the excitation process in atomic hydrogen or in a hydrogen like ionwith low nuclear charge number in the presence of the circularly polarizedlaser light. The derived formula for the dynamic AC Stark shift of hydrogenicenergy levels using these two methods are shown to be same in the limit oflarge photon numbers.

Dynamic Stark shift of Hydrogen-like atoms in the presence of circularly polarized laser light