International Journal of Theoretical Physics

, Volume 49, Issue 5, pp 1106–1117 | Cite as

Excited Two-Mode Generalized Squeezed Vacuum State as a Squeezed Two-Variable Hermite Polynomial Excitation State

Article
First Online:
Received:
Accepted:

Abstract

A new class of excited two-mode generalized squeezed vacuum states denoted by |r,s,m,n〉 are presented, which are obtained by repeatedly applying creation operators a † and b † on the two-mode generalized squeezed vacuum state. We find that it is just regarded as a generalized squeezed two-variable Hermite polynomial excitation on the vacuum state and its normalization constant is just a Jacobi polynomial. Their statistical properties are investigated such as squeezing properties, photon number distribution and the violations of Cauchy-Schwartz inequality. Especially, the Wigner function for |r,s,m,n〉 depending on the excitation photon numbers is discussed graphically.

Keywords

Two-mode generalized squeezed vacuum state Two-variable Hermite polynomial Violations of Cauchy-Schwartz inequality Wigner function 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Loudon, R., Knight, P.L.: J. Mod. Opt. 34, 709 (1987) MATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Buzek, V.: J. Mod. Opt. 37, 303 (1990) MATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    Dodonov, V.V.: J. Opt. B Quantum Semiclass. Opt. 4, R1 (2002) CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Schrade, G., Akulin, V.M., Man’ko, V.I., Schleich, W.P.: Phys. Rev. A 48, 2398 (1993) CrossRefADSGoogle Scholar
  5. 5.
    Gantsog, T., Tanaś, R.: Phys. Lett. A 152, 251 (1991) CrossRefADSGoogle Scholar
  6. 6.
    Chizhov, A.V., Murzakhmetov, B.K.: Phys. Lett. A 176, 33 (1993) CrossRefADSGoogle Scholar
  7. 7.
    Selvadoray, M., Kumar, M.S.: Opt. Commun. 136, 125 (1997) CrossRefADSGoogle Scholar
  8. 8.
    Hiroshima, T.: Phys. Rev. A 63, 022305 (2001) CrossRefADSGoogle Scholar
  9. 9.
    Ban, M.: J. Opt. B Quantum Semiclass. Opt. 1, L9 (1999) CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Hu, L.Y., Fan, H.Y.: Commun. Theor. Phys. 50, 965 (2008) CrossRefGoogle Scholar
  11. 11.
    Ban, M.: J. Opt. B Quantum Semiclass. Opt. 7, L4 (2005) CrossRefADSGoogle Scholar
  12. 12.
    Schumaker, B.L.: Phys. Rep. 135, 317 (1986) CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Abdalla, M.S.: J. Mod. Opt. 39, 1067 (1992) MATHCrossRefMathSciNetADSGoogle Scholar
  14. 14.
    Hu, L.Y., Fan, H.Y.: J. Mod. Opt. 5513, 2011 (2008) CrossRefADSGoogle Scholar
  15. 15.
    Agarwal, G.S., Tara, K.: Phys. Rev. A 43, 492 (1991) CrossRefADSGoogle Scholar
  16. 16.
    Hu, L.Y., Fan, H.Y.: Phys. Scr. 79, 035004 (2009) CrossRefADSGoogle Scholar
  17. 17.
    Zhang, Z.X., Fan, H.Y.: Phys. Lett. A 165, 14 (1992) CrossRefMathSciNetADSGoogle Scholar
  18. 18.
    Meng, X.G., Wang, J.S., Fan, H.Y.: Phys. Lett. A 361, 183 (2007) MATHCrossRefMathSciNetADSGoogle Scholar
  19. 19.
    Meng, X.G., Wang, J.S., Liang, B.L., Li, H.Q.: Chin. Phys. B 17, 1791 (2008) CrossRefADSGoogle Scholar
  20. 20.
    Yuan, H.C., Xu, X.X., Fan, H.Y.: Int. J. Theor. Phys. 48, 3596 (2009) MATHCrossRefGoogle Scholar
  21. 21.
    Dai, Q., Jing, H.: Int. J. Theor. Phys. 47, 2716 (2008) MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Li, H.M., Yuan, H.C., Fan, H.Y.: Int. J. Theor. Phys. 48, 2849 (2009) MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Fan, H.Y., Lu, H.L.: Phys. Lett. A 334, 132 (2005) MATHCrossRefADSGoogle Scholar
  24. 24.
    Fan, H.Y., Chen, J.H.: Commun. Theor. Phys. 40, 589 (2003) MATHMathSciNetGoogle Scholar
  25. 25.
    Fan, H.Y.: J. Opt. B Quantum Semiclass. Opt. 5, R147 (2003) CrossRefADSGoogle Scholar
  26. 26.
    Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd edn. Springer, Berlin (1966) MATHGoogle Scholar
  27. 27.
    Erdelyi, A.: Higher Transcendental Functions. McGraw-Hill, New York (1995) Google Scholar
  28. 28.
    Loudon, R.: Rep. Prog. Phys. 43, 913 (1980) CrossRefMathSciNetADSGoogle Scholar
  29. 29.
    Fan, H.Y., Lu, H.L.: J. Opt. Soc. Am. B 25, 1955 (2008) CrossRefADSGoogle Scholar
  30. 30.
    Fan, H.Y.: Ann. Phys. 323, 500 (2008) MATHCrossRefADSGoogle Scholar
  31. 31.
    Fan, H.Y.: J. Phys. A Math. Gen. 25, 3443 (1992) MATHCrossRefGoogle Scholar
  32. 32.
    Kenfack, A., Zyczkowski, K.: J. Opt. B Quantum Semiclass. Opt. 6, 396 (2004) CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Modern PhysicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Department of PhysicsShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations