We compare the derivation of the dynamic Stark shift of hydrogenic energy levels in a classical framework with an adiabatically damped laser-atom interaction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a treatment based on time-independent perturbation theory, with a second-quantized laser-atom dipole interaction Hamiltonian. Our analysis applies to a laser that excites a two-photon transition in atomic hydrogen or in a hydrogenlike ion with low nuclear charge number. Our comparisons serve to demonstrate why the dynamic Stark shift may be interpreted as a stimulated radiative correction and illustrates connections between the two derivations. The simplest of the derivations is the fully quantized approach. The classical and the second-quantized treatment are shown to be equivalent in the limit of large photon numbers.
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PAPERS| January 01 2006
Comparison of classical and second quantized description of the dynamic Stark shift
U. D. Jentschura;
M. Haas, U. D. Jentschura, C. H. Keitel; Comparison of classical and second quantized description of the dynamic Stark shift. Am. J. Phys. 1 January 2006; 74 (1): 77–81. https://doi.org/10.1119/1.2140742
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