Barut–Girardello and Gilmore–Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties：Factorization method

doi:10.1088/1674-1056/22/8/084202

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 84202-084202.doi: 10.1088/1674-1056/22/8/084202

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Barut–Girardello and Gilmore–Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties：Factorization method

M K Tavassoly^{a b c}, H R Jalali^a

a Atomic and Molecular Group, Faculty of Physics, Yazd University, Yazd, Iran;
b Photonics Research Group, Engineering Research Center, Yazd University, Yazd, Iran;
c The Laboratory of Quantum Information Processing, Yazd University, Yazd, Iran

收稿日期:2012-12-12 修回日期:2013-01-30 出版日期:2013-06-27 发布日期:2013-06-27

Barut–Girardello and Gilmore–Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties：Factorization method

M K Tavassoly^{a b c}, H R Jalali^a

a Atomic and Molecular Group, Faculty of Physics, Yazd University, Yazd, Iran;
b Photonics Research Group, Engineering Research Center, Yazd University, Yazd, Iran;
c The Laboratory of Quantum Information Processing, Yazd University, Yazd, Iran

Received:2012-12-12 Revised:2013-01-30 Online:2013-06-27 Published:2013-06-27
Contact: M K Tavassoly E-mail:mktavassoly@yazd.ac.ir

摘要/Abstract

摘要： In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schrödinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU(1,1) dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.

关键词: pseudoharmonic oscillator, factorization method, Barut-Girardello coherent states, Gilmore-Perelomov coherent states, nonclassical properties

Abstract: In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schrödinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU(1,1) dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.

Key words: pseudoharmonic oscillator, factorization method, Barut-Girardello coherent states, Gilmore-Perelomov coherent states, nonclassical properties

中图分类号: (Quantum state engineering and measurements)

42.50.Dv

42.50.-p (Quantum optics)

M K Tavassoly, H R Jalali. Barut–Girardello and Gilmore–Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties：Factorization method[J]. 中国物理B, 2013, 22(8): 84202-084202.

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Barut–Girardello and Gilmore–Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties：Factorization method

Barut–Girardello and Gilmore–Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties：Factorization method

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