dorsal/arxiv
View SchemaAn exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: the Casimir-Polder potential
| Authors | F. Ciccarello, E. Karpov, R. Passante |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508034 |
| URL | https://arxiv.org/abs/quant-ph/0508034 |
| DOI | 10.1103/PhysRevA.72.052106 |
| Journal | Physical Review A 72, 052106 (2005) |
Abstract
We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift the nonperturbative Casimir-Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expression of the Casimir-Polder potential in terms of the polarizabilities of the oscillators is recovered.
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"abstract": "We consider two three-dimensional isotropic harmonic oscillators interacting\nwith the quantum electromagnetic field in the Coulomb gauge and within dipole\napproximation. Using a Bogoliubov-like transformation, we can obtain\ntransformed operators such that the Hamiltonian of the system, when expressed\nin terms of these operators, assumes a diagonal form. We are also able to\nobtain an expression for the energy shift of the ground state, which is valid\nat all orders in the coupling constant. From this energy shift the\nnonperturbative Casimir-Polder potential energy between the two oscillators can\nbe obtained. When approximated to the fourth order in the electric charge, the\nwell-known expression of the Casimir-Polder potential in terms of the\npolarizabilities of the oscillators is recovered.",
"arxiv_id": "quant-ph/0508034",
"authors": [
"F. Ciccarello",
"E. Karpov",
"R. Passante"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.052106",
"journal_ref": "Physical Review A 72, 052106 (2005)",
"title": "An exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: the Casimir-Polder potential",
"url": "https://arxiv.org/abs/quant-ph/0508034"
},
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