dorsal/arxiv
View SchemaGeneralized Hypergeometric Coherent States
| Authors | T. Appl, D. H. Schiller |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308013 |
| URL | https://arxiv.org/abs/quant-ph/0308013 |
| DOI | 10.1088/0305-4470/37/7/015 |
Abstract
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disk, and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg-Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce generalized hypergeometric Husimi distributions and corresponding phase distributions as well as new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces.
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"abstract": "We introduce a large class of holomorphic quantum states by choosing their\nnormalization functions to be given by generalized hypergeometric functions. We\ncall them generalized hypergeometric states in general, and generalized\nhypergeometric coherent states in particular, if they allow a resolution of\nunity. Depending on the domain of convergence of the generalized hypergeometric\nfunctions, we distinguish generalized hypergeometric states on the plane, the\nopen unit disk, and the unit circle. All states are eigenstates of suitably\ndefined lowering operators. We then study their photon number statistics and\nphase properties as revealed by the Husimi and Pegg-Barnett phase\ndistributions. On the basis of the generalized hypergeometric coherent states\nwe introduce generalized hypergeometric Husimi distributions and corresponding\nphase distributions as well as new analytic representations of arbitrary\nquantum states in Bargmann and Hardy spaces.",
"arxiv_id": "quant-ph/0308013",
"authors": [
"T. Appl",
"D. H. Schiller"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/37/7/015",
"title": "Generalized Hypergeometric Coherent States",
"url": "https://arxiv.org/abs/quant-ph/0308013"
},
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