dorsal/arxiv
View SchemaComparison of classical and second quantized description of the dynamic Stark shift
| Authors | M. Haas, U. D. Jentschura, C. H. Keitel |
|---|---|
| Categories | |
| ArXiv ID | physics/0510160 |
| URL | https://arxiv.org/abs/physics/0510160 |
| DOI | 10.1119/1.2140742 |
| Journal | Am. J. Phys. 74 (2006) 77-81 |
Abstract
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.
{
"annotation_id": "84d749a0-f669-4e7e-b525-6bd0a94cbf32",
"date_created": "2026-03-02T18:01:03.482000Z",
"date_modified": "2026-03-02T18:01:03.482000Z",
"file_hash": "0170f35e5abe28fd020643f163929ee2fa0b9aab362951dfdf539d019416a87d",
"private": false,
"record": {
"abstract": "We compare the derivation of the dynamic Stark shift of hydrogenic energy\nlevels in a classical framework with an adiabatically damped laser-atom\ninteraction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a\ntreatment based on time-independent perturbation theory, with a\nsecond-quantized laser-atom dipole interaction Hamiltonian. Our analysis\napplies to a laser that excites a two-photon transition in atomic hydrogen or\nin a hydrogenlike ion with low nuclear charge number. Our comparisons serve to\ndemonstrate why the dynamic Stark shift may be interpreted as a stimulated\nradiative correction and illustrates connections between the two derivations.\nThe simplest of the derivations is the fully quantized approach. The classical\nand the second-quantized treatment are shown to be equivalent in the limit of\nlarge photon numbers.",
"arxiv_id": "physics/0510160",
"authors": [
"M. Haas",
"U. D. Jentschura",
"C. H. Keitel"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1119/1.2140742",
"journal_ref": "Am. J. Phys. 74 (2006) 77-81",
"title": "Comparison of classical and second quantized description of the dynamic Stark shift",
"url": "https://arxiv.org/abs/physics/0510160"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "2cc00f9c-c49a-4b1c-9ed6-a7585f4286c4",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}