International Journal of Theoretical Physics

, Volume 47, Issue 5, pp 1147–1155 | Cite as

Three-Mode Nonlinear Bogoliubov Transformations



We introduce the three-mode nonlinear Bogoliubov transformations based on the work of Siena et al. (Phys. Rev. A 64:063803, 2001) and Ying Wu (Phys. Rev. A 66:025801, 2002) about nonlinear Bogoliubov transformations. We show that three-mode nonlinear Bogoliubov transformations can be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. Such decomposition turns all the nonlinear canonic coordinate-dependent Bogoliubov transformations into essentially linear problems as we shall prove and hence greatly facilitate calculations of the properties and the quantities related to the nonlinear transformations.


Coordinate-dependent three-mode nonlinear Bogoliubov transformations Three-mode squeezed states 


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  1. 1.
    De Siena, S., Di Lisi, A., Illuminati, F.: Phys. Rev. A 64, 063803 (2001) CrossRefADSGoogle Scholar
  2. 2.
    Wu, Y., Cote, R.: Phys. Rev. A 66, 025801 (2002) CrossRefADSGoogle Scholar
  3. 3.
    Fan, H., Jiang, N., Lu, H.: Mod. Phys. Lett. B 16, 1193 (2002) MATHCrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Walls, D.F., Milburn, G.J.: Quantum Optics. Springer, New York (1986) Google Scholar
  5. 5.
    Wu, Y.: Phys. Rev. A 54, 4534 (1996) CrossRefADSGoogle Scholar
  6. 6.
    Wu, Y.: Phys. Rev. A 54, 1586 (1996) CrossRefADSGoogle Scholar
  7. 7.
    Perelomov, A.: Generalized Coherent States and Their Applications. Springer, New York (1986) MATHGoogle Scholar
  8. 8.
    Yuen, H.P.: Phys. Rev. A 13, 226 (1976) CrossRefGoogle Scholar
  9. 9.
    Wu, Y., Yang, X.: J. Phys. A 34, 327 (2001) MATHCrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Wu, Y., Yang, X.: Phys. Rev. A 63, 043816 (2001) CrossRefADSGoogle Scholar
  11. 11.
    Wallentowitz, S., Vogel, W., Knight, P.L.: Phys. Rev. A 59, 531 (1999) CrossRefADSGoogle Scholar
  12. 12.
    Sachdev, S.: Quantum Phase Transitions. Cambridge University Press, New York (2000) MATHGoogle Scholar

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsNingbo UniversityNingboChina

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