• Chinese Journal of Quantum Electronics
  • Vol. 31, Issue 2, 135 (2014)
Jian-min CHENG*, Xiu-dong LIANG, Zheng-fang ZHU, Wei-feng WU, and Ye-jun XU
Author Affiliations
  • [in Chinese]
  • show less
    DOI: 10.3969/j.issn.1007-5461.2014.02.002 Cite this Article
    CHENG Jian-min, LIANG Xiu-dong, ZHU Zheng-fang, WU Wei-feng, XU Ye-jun. Eigenkets of abnormal Boson creation operator[J]. Chinese Journal of Quantum Electronics, 2014, 31(2): 135 Copy Citation Text show less
    References

    [1] Xie C M, Fan H Y. Application of the two-mode squeezed coherent state representation in deriving generalized optical Collins formula [J]. Optik, 2011, 122: 949-954.

    [4] van Enk SJ, Hirota O. Entangled coherent states: Teleportation and decoherence [J]. Phys. Rev. A, 2001, 64: 022313.

    [5] Cheong Y W, Kim H, Lee H W. Near-complete teleportation of a superposed coherent state [J]. Phys. Rev. A, 2004, 70: 032327.

    [6] Sanders B C, Bartlett S D. Photon-number superselection and the entangled coherent-state representation [J]. Phys. Rev. A, 2003, 68: 042329.

    [7] Gerrits T, Glancy S, Clement T S, et al. Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum [J]. Phys. Rev. A, 2010, 82: 031802(R).

    [8] Loock P V, Lütkenhaus N, Munro W J, et al. Quantum repeaters using coherent-state communication [J]. Phys. Rev. A, 2008, 78: 062319.

    [9] Cappellaro P, Viola L, Ramanathan C. Coherent-state transfer via highly mixed quantum spin chains [J]. Phys. Rev. A, 2011, 83: 032304.

    [10] Heid M, Lütkenhaus N. Security of coherent-state quantum cryptography in the presence of Gaussian noise [J]. Phys. Rev. A, 2007, 76: 022313.

    [11] Davydov A S. Quantum Mechanics[M]. 2nd ed, Oxford: Pergamon Press, 1976.

    [12] Heitler W. The Quantum Theory of Radiation [M], 3rd ed, London: Oxford Claredon Press, 1954.

    [13] Fan H Y, Xiao M. Dual eigenkets of the Susskind-Glogower phase operator [J]. Phys. Rev. A, 1996, 54: 5295-5298.

    [14] Xu Y J, Song J, Fan H Y, et al. Eigenkets of the q-deformed creation operator [J]. J. Math. Phys., 2010, 51: 092107.

    [15] Fan H Y, Wünsche A. Eigenstates of Boson creation operator [J]. Eur. Phys. J. D, 2001, 15: 405-412.

    [16] Fan H Y, et al. Dual state vector of nonlinear coherent state and its application in complex P-representation [J]. J. Phys. A: Math. Gen., 2001, 34: 6127.

    [17] Fan H Y, et al. Complex P representation of the density matrix obtained via creation operator eigenvectors [J]. Phys. Lett. A, 1996, 219: 175-179.

    [19] Bie H D, Sommen F. Hermite and Gegenbauer polynomials in superspace using Clifford analysis [J]. J. Phys. A: Math. Theor., 2007, 40: 34.

    [20] Odakea S, Sasakib R. q-oscillator from the q-Hermite polynomial [J]. Phys. Lett. B, 2008, 663: 141-145.

    [21] Meng X G, Wang J S, Li Y L. Wigner function and tomogram of the Hermite polynomial state [J]. Chin. Phys., 2007, 16: 2415.

    [22] Thirulogasanthar K, Honnouvo G, Krzy ak A. Coherent states and Hermite polynomials on quaternionic Hilbert spaces [J]. J. Phys. A: Math. Theor., 2010, 43: 385205.

    [23] Cotfas N, Gazeau J P, Katarzyna G. Complex and real Hermite polynomials and related quantizations [J]. J. Phys. A: Math. Theor., 2010, 43: 305304.

    [24] Kasraoui A, Stanton D, Zenga J. The combinatorics of Al-Salam-Chihara q-Laguerre polynomials [J]. Adv. Appl. Math., 2011, 47: 216-239.

    [25] Ho C L. Dirac(-Pauli), Fokker-Plank equation and exceptional Laguerre polynomials [J]. Ann. Phys., 2011, 326: 797-807.

    [26] David G U, Kamran N, Milson R. Two-step Darboux transformations and exceptional Laguerre polynomials [J]. J. Math. Anal. Appl., 2012, 387: 410-418.

    [27] Sasaki R, Tsujimoto S, Zhedanov A. Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum transformations [J]. J. Phys. A: Math. Theor., 2010, 43: 315204.

    [28] Odake S, Sasaki R. Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials [J]. J. Math. Phys., 2010, 51: 053513.

    [29] Odakea S, Sasakib R. Another set of infinitely many exceptional (X ) Laguerre polynomials [J]. Phys. Lett. B, 2010, 684: 173-176.

    CHENG Jian-min, LIANG Xiu-dong, ZHU Zheng-fang, WU Wei-feng, XU Ye-jun. Eigenkets of abnormal Boson creation operator[J]. Chinese Journal of Quantum Electronics, 2014, 31(2): 135
    Download Citation