dorsal/arxiv
View SchemaOn the squeezed states for n observables
| Authors | D. A. Trifonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9705001 |
| URL | https://arxiv.org/abs/quant-ph/9705001 |
| DOI | 10.1088/0031-8949/58/3/009 |
| Journal | Phys.Scripta 58 (1998) 246-255 |
Abstract
Three basic properties (eigenstate, orbit and intelligence) of the canonical squeezed states (SS) are extended to the case of arbitrary n observables. The SS for n observables X_i can be constructed as eigenstates of their linear complex combinations or as states which minimize the Robertson uncertainty relation. When X_i close a Lie algebra L the generalized SS could also be introduced as orbit of Aut(L^C). It is shown that for the nilpotent algebra h_N the three generalizations are equivalent. For the simple su(1,1) the family of eigenstates of uK_- + vK_+ (K_\pm being lowering and raising operators) is a family of ideal K_1-K_2 SS, but it cannot be represented as an Aut(su^C(1,1)) orbit although the SU(1,1) group related coherent states (CS) with symmetry are contained in it. Eigenstates |z,u,v,w;k> of general combination uK_- + vK_+ + wK_3 of the three generators K_j of SU(1,1) in the representations with Bargman index k = 1/2,1, ..., and k = 1/4,3/4 are constructed and discussed in greater detail. These are ideal SS for K_{1,2,3}. In the case of the one mode realization of su(1,1) the nonclassical properties (sub-Poissonian statistics, quadrature squeezing) of the generalized even CS |z,u,v;+> are demonstrated. The states |z,u,v,w;k=1/4,3/4> can exhibit strong both linear and quadratic squeezing.
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"abstract": "Three basic properties (eigenstate, orbit and intelligence) of the canonical\nsqueezed states (SS) are extended to the case of arbitrary n observables. The\nSS for n observables X_i can be constructed as eigenstates of their linear\ncomplex combinations or as states which minimize the Robertson uncertainty\nrelation. When X_i close a Lie algebra L the generalized SS could also be\nintroduced as orbit of Aut(L^C). It is shown that for the nilpotent algebra h_N\nthe three generalizations are equivalent. For the simple su(1,1) the family of\neigenstates of uK_- + vK_+ (K_\\pm being lowering and raising operators) is a\nfamily of ideal K_1-K_2 SS, but it cannot be represented as an Aut(su^C(1,1))\norbit although the SU(1,1) group related coherent states (CS) with symmetry are\ncontained in it.\n Eigenstates |z,u,v,w;k\u003e of general combination uK_- + vK_+ + wK_3 of the\nthree generators K_j of SU(1,1) in the representations with Bargman index k =\n1/2,1, ..., and k = 1/4,3/4 are constructed and discussed in greater detail.\nThese are ideal SS for K_{1,2,3}. In the case of the one mode realization of\nsu(1,1) the nonclassical properties (sub-Poissonian statistics, quadrature\nsqueezing) of the generalized even CS |z,u,v;+\u003e are demonstrated. The states\n|z,u,v,w;k=1/4,3/4\u003e can exhibit strong both linear and quadratic squeezing.",
"arxiv_id": "quant-ph/9705001",
"authors": [
"D. A. Trifonov"
],
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"quant-ph"
],
"doi": "10.1088/0031-8949/58/3/009",
"journal_ref": "Phys.Scripta 58 (1998) 246-255",
"title": "On the squeezed states for n observables",
"url": "https://arxiv.org/abs/quant-ph/9705001"
},
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