dorsal/arxiv
View SchemaOn the Preparation of Pure States in Resonant Microcavities
| Authors | Per K. Rekdal, Bo-Sture K. Skagerstam, Peter L. Knight |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301148 |
| URL | https://arxiv.org/abs/quant-ph/0301148 |
| DOI | 10.1080/09500340408234593 |
Abstract
We consider the time evolution of the radiation field (R) and a two-level atom (A) in a resonant microcavity in terms of the Jaynes-Cummings model with an initial general pure quantum state for the radiation field. It is then shown, using the Cauchy-Schwarz inequality and also a Poisson resummation technique, that {\it perfect} coherence of the atom can in general never be achieved. The atom and the radiation field are, however, to a good approximation in a pure state $|\psi >_A\otimes|\psi >_R$ in the middle of what has been traditionally called the ``collapse region'', independent of the initial state of the atoms, provided that the initial pure state of the radiation field has a photon number probability distribution which is sufficiently peaked and phase differences that do not vary significantly around this peak. An approximative analytic expression for the quantity $\Tr[\rho^2_{A}(t)]$, where $\rho_{A}(t)$ is the reduced density matrix for the atom, is derived. We also show that under quite general circumstances an initial entangled pure state will be disentangled to the pure state $|\psi >_{A\otimes R}$.
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"abstract": "We consider the time evolution of the radiation field (R) and a two-level\natom (A) in a resonant microcavity in terms of the Jaynes-Cummings model with\nan initial general pure quantum state for the radiation field. It is then\nshown, using the Cauchy-Schwarz inequality and also a Poisson resummation\ntechnique, that {\\it perfect} coherence of the atom can in general never be\nachieved. The atom and the radiation field are, however, to a good\napproximation in a pure state $|\\psi \u003e_A\\otimes|\\psi \u003e_R$ in the middle of what\nhas been traditionally called the ``collapse region\u0027\u0027, independent of the\ninitial state of the atoms, provided that the initial pure state of the\nradiation field has a photon number probability distribution which is\nsufficiently peaked and phase differences that do not vary significantly around\nthis peak. An approximative analytic expression for the quantity\n$\\Tr[\\rho^2_{A}(t)]$, where $\\rho_{A}(t)$ is the reduced density matrix for the\natom, is derived. We also show that under quite general circumstances an\ninitial entangled pure state will be disentangled to the pure state $|\\psi\n\u003e_{A\\otimes R}$.",
"arxiv_id": "quant-ph/0301148",
"authors": [
"Per K. Rekdal",
"Bo-Sture K. Skagerstam",
"Peter L. Knight"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/09500340408234593",
"title": "On the Preparation of Pure States in Resonant Microcavities",
"url": "https://arxiv.org/abs/quant-ph/0301148"
},
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