dorsal/arxiv
View SchemaRobertson Intelligent States
| Authors | D. A. Trifonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9701018 |
| URL | https://arxiv.org/abs/quant-ph/9701018 |
| DOI | 10.1088/0305-4470/30/17/006 |
| Journal | J.Phys.A30:5941-5957,1997 |
Abstract
Diagonalization of uncertainty matrix and minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear combinations of the observables. In case of canonical observables this eigenvalue condition is also necessary. Such minimizing states are called Robertson intelligent states (RIS). The group related coherent states (CS) with maximal symmetry (for semisimple Lie groups) are particular case of RIS for the quadratures of Weyl generators. Explicit constructions of RIS are considered for operators of su(1,1), su(2), h_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong squeezing of group generators. Multimode squared amplitude squeezed states are naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices for quadratures of q-deformed boson operators a_{q,j} (q > 0) and of any k power of a_j = a_{1,j} are positive definite and can be diagonalized by symplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.Dv
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"abstract": "Diagonalization of uncertainty matrix and minimization of Robertson\ninequality for n observables are considered. It is proved that for even n this\nrelation is minimized in states which are eigenstates of n/2 independent\ncomplex linear combinations of the observables. In case of canonical\nobservables this eigenvalue condition is also necessary. Such minimizing states\nare called Robertson intelligent states (RIS).\n The group related coherent states (CS) with maximal symmetry (for semisimple\nLie groups) are particular case of RIS for the quadratures of Weyl generators.\nExplicit constructions of RIS are considered for operators of su(1,1), su(2),\nh_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong\nsqueezing of group generators. Multimode squared amplitude squeezed states are\nnaturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices\nfor quadratures of q-deformed boson operators a_{q,j} (q \u003e 0) and of any k\npower of a_j = a_{1,j} are positive definite and can be diagonalized by\nsymplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.Dv",
"arxiv_id": "quant-ph/9701018",
"authors": [
"D. A. Trifonov"
],
"categories": [
"quant-ph",
"cond-mat",
"nucl-th"
],
"doi": "10.1088/0305-4470/30/17/006",
"journal_ref": "J.Phys.A30:5941-5957,1997",
"title": "Robertson Intelligent States",
"url": "https://arxiv.org/abs/quant-ph/9701018"
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