dorsal/arxiv
View SchemaExact solutions to the time-dependent supersymmetric muliphoton Jaynes-Cummings model and the Chiao-Wu model
| Authors | Jian-Qi Shen, Hong-Yi Zhu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305057 |
| URL | https://arxiv.org/abs/quant-ph/0305057 |
| DOI | 10.1002/andp.200310001 |
| Journal | Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-145 |
Abstract
By using both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside the optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schr\"{o}dinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.
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"abstract": "By using both the Lewis-Riesenfeld invariant theory and the invariant-related\nunitary transformation formulation, the present paper obtains the exact\nsolutions to the time-dependent supersymmetric two-level multiphoton\nJaynes-Cummings model and the Chiao-Wu model that describes the propagation of\na photon inside the optical fiber. On the basis of the fact that the two-level\nmultiphoton Jaynes-Cummings model possesses the supersymmetric structure, an\ninvariant is constructed in terms of the supersymmetric generators by working\nin the sub-Hilbert-space corresponding to a particular eigenvalue of the\nconserved supersymmetric generators (i.e., the time-independent invariant). By\nconstructing the effective Hamiltonian that describes the interaction of the\nphoton with the medium of the optical fiber, it is further verified that the\nparticular solution to the Schr\\\"{o}dinger equation is the eigenfunction of the\nsecond-quantized momentum operator of photons field. This, therefore, means\nthat the explicit expression (rather than the hidden form that involves the\nchronological product) for the time-evolution operator of wave function is\nobtained by means of the invariant theories.",
"arxiv_id": "quant-ph/0305057",
"authors": [
"Jian-Qi Shen",
"Hong-Yi Zhu"
],
"categories": [
"quant-ph"
],
"doi": "10.1002/andp.200310001",
"journal_ref": "Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-145",
"title": "Exact solutions to the time-dependent supersymmetric muliphoton Jaynes-Cummings model and the Chiao-Wu model",
"url": "https://arxiv.org/abs/quant-ph/0305057"
},
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