Comparison of classical and second quantized description of the dynamic Stark shift

M. Haas, U. D. Jentschura, C. H. Keitel

Research output: Contribution to journalArticle

27 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)77-81
Number of pages5
JournalAmerican Journal of Physics
Issue number1
Publication statusPublished - Jan 1 2006

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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