dorsal/arxiv
View SchemaTheory of dressed states in quantum optics
| Authors | Marco Frasca |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9811037 |
| URL | https://arxiv.org/abs/quant-ph/9811037 |
| DOI | 10.1103/PhysRevA.60.573 |
| Journal | Phys.Rev. A60 (1999) 573-581 |
Abstract
The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both Dyson series and its dual, through renormalization group methods to remove secular terms from the perturbation series, give the opportunity of a full study of the solution of the Schr\"{o}dinger equation in different ranges of the parameters of the given hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to exploit the method at the best, a study is accomplished of the well-known Jaynes-Cummings model in the rotating wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is needed to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.
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"abstract": "The dual Dyson series [M.Frasca, Phys. Rev. A {\\bf 58}, 3439 (1998)], is used\nto develop a general perturbative method for the study of atom-field\ninteraction in quantum optics. In fact, both Dyson series and its dual, through\nrenormalization group methods to remove secular terms from the perturbation\nseries, give the opportunity of a full study of the solution of the\nSchr\\\"{o}dinger equation in different ranges of the parameters of the given\nhamiltonian. In view of recent experiments with strong laser fields, this\napproach seems well-suited to give a clarification and an improvement of the\napplications of the dressed states as currently done through the eigenstates of\nthe atom-field interaction, showing that these are just the leading order of\nthe dual Dyson series when the Hamiltonian is expressed in the interaction\npicture. In order to exploit the method at the best, a study is accomplished of\nthe well-known Jaynes-Cummings model in the rotating wave approximation, whose\nexact solution is known, comparing the perturbative solutions obtained by the\nDyson series and its dual with the same approximations obtained by Taylor\nexpanding the exact solution. Finally, a full perturbative study of high-order\nharmonic generation is given obtaining, through analytical expressions, a clear\naccount of the power spectrum using a two-level model, even if the method can\nbe successfully applied to a more general model that can account for ionization\ntoo. The analysis shows that to account for the power spectrum it is needed to\ngo to first order in the perturbative analysis. The spectrum obtained gives a\nway to measure experimentally the shift of the energy levels of the atom\ninteracting with the laser field by looking at the shifting of hyper-Raman\nlines.",
"arxiv_id": "quant-ph/9811037",
"authors": [
"Marco Frasca"
],
"categories": [
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],
"doi": "10.1103/PhysRevA.60.573",
"journal_ref": "Phys.Rev. A60 (1999) 573-581",
"title": "Theory of dressed states in quantum optics",
"url": "https://arxiv.org/abs/quant-ph/9811037"
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