\(su(1,1)\) intelligent states. (English) Zbl 1198.81224
Summary: We construct all the intelligent states of the non-compact generators of \(su(1,1)\) for every positive discrete representation of this Lie algebra, and discuss some of the properties of these states.
MSC:
| 81V80 | Quantum optics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
References:
| [1] | Gerry C C and Knight P L 2005 Introductory Quantum Optics (Cambridge: Cambridge University Press) |
| [2] | Wódkiewicz K and Eberly J H 1985 J. Opt. Soc. Am. B 2 458 · doi:10.1364/JOSAB.2.000458 |
| [3] | see for instance Shaterzadeh-Yazdi Z et al 2008 J. Phys. A: Math. Theor.41 055309 · Zbl 1134.81382 · doi:10.1088/1751-8113/41/5/055309 |
| [4] | Bartlett S D et al 2001 Phys. Rev. A 63 042310 · doi:10.1103/PhysRevA.63.042310 |
| [5] | Vourdas A 1992 Phys. Rev. A 45 1943 · doi:10.1103/PhysRevA.45.1943 |
| [6] | Vourdas A 1990 Phys. Rev. A 41 1653 · doi:10.1103/PhysRevA.41.1653 |
| [7] | Ui H 1968 Ann. Phys., NY49 69 · doi:10.1016/0003-4916(68)90184-X |
| [8] | Solomon A I 1971 J. Math. Phys.12 390 · doi:10.1063/1.1665601 |
| [9] | Armstrong L Jr 1971 J. Math. Phys.12 935 · doi:10.1063/1.1665687 |
| [10] | Yonte T et al 2002 J. Opt. Soc. Am.19 603 · doi:10.1364/JOSAA.19.000603 |
| [11] | Barriuso A G et al 2003 J. Opt. Soc. Am.20 1812 · doi:10.1364/JOSAA.20.001812 |
| [12] | Biedenharn L C and Louck J D 1985 The Racah-Wigner Algebra in Quantum Theory(Encyclopedia of Mathematics vol 9) (New York: Cambridge University Press) |
| [13] | Jackiw R 1968 J. Math. Phys.9 339 · Zbl 0159.59801 · doi:10.1063/1.1664585 |
| [14] | Lavoie B R et al 2007 J. Phys. A: Math. Theor.40 2825 · Zbl 1111.81103 · doi:10.1088/1751-8113/40/11/017 |
| [15] | Mahler D et al 2010 New J. Phys.12 033037 · doi:10.1088/1367-2630/12/3/033037 |
| [16] | Agarwal G S and Puri R R 1994 Phys. Rev. A 49 4968 · doi:10.1103/PhysRevA.49.4968 |
| [17] | Bergou J A et al 1991 Phys. Rev. A 43 515 · doi:10.1103/PhysRevA.43.515 |
| [18] | Satya Prakash G and Agarwal G S 1994 Phys. Rev. A 50 4258 · doi:10.1103/PhysRevA.50.4258 |
| [19] | Satya Prakash G and Agarwal G S 1995 Phys. Rev. A 52 2335 · doi:10.1103/PhysRevA.52.2335 |
| [20] | Puri R R and Agarwal G S 1996 Int. J. Mod. Phys. B 10 1563 · Zbl 1229.81124 · doi:10.1142/S0217979296000660 |
| [21] | Ui H 1970 Prog. Theor. Phys.44 689 · Zbl 1098.81709 · doi:10.1143/PTP.44.689 |
| [22] | Abd Al Kader G M and Obada A-S F 2008 Phys. Scr.78 035401 · Zbl 1145.81377 · doi:10.1088/0031-8949/78/03/035401 |
| [23] | Brif C and Mann A 1996 Phys. Rev. A 54 4505 · doi:10.1103/PhysRevA.54.4505 |
| [24] | Luis A and Peřina J 1996 Phys. Rev. A 53 1886 · doi:10.1103/PhysRevA.53.1886 |
| [25] | Biedenharn L C et al 1965 Ann. Inst. Henri Poincaré3 13 |
| [26] | Van der Jeugt J 1997 J. Math. Phys.38 2728 · Zbl 0897.17005 · doi:10.1063/1.531984 |
| [27] | Kitagawa M and Ueda M 1993 Phys. Rev. A 47 5138 · doi:10.1103/PhysRevA.47.5138 |
| [28] | Luis A and Korolkova N 2006 Phys. Rev. A 74 043817 · doi:10.1103/PhysRevA.74.043817 |
| [29] | Boas M L 2006 Mathematical Methods in the Physical Sciences 3rd edn (New York: Wiley) · Zbl 1088.00002 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
