Skip to main content
SpringerLink
Log in

Non-positiveWigner Function and Non-Gaussianty Generated by Multiple Creation-then-annihilation Coherent State

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We investigate the nonclassicality of a kind of quantum state (MPCACS) generated by repeatedly operating creation-then-annihilation (CA) on the coherent state (CS). Its normalization factor is arduously derived in compact expression related to the Laguerre-polynomial. We explore two observable nonclassical properties of MPCACS, such as non-positive Wigner function and non-Guassianty, which exhibit their highly nonclassical behaviors depending on m. Here, we adopt the Hilbert-Schmidt distance to quantify its Non-Gaussian characters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Dodonov, V.V.: J. Opt. B: Quantum Semiclass. Opt. 4, R1–R33 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  2. Dell’Anno, F., Siena, S.D., Illuminati, F.: Phys. Rep. 428, 53–168 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  3. Short, R., Mandel, L.: Phys. Rev. Lett. 51, 384 (1983)

    Article  ADS  Google Scholar 

  4. Hong, C.K., Mandel, L.: Phys. Rev. Lett. 54, 323 (1985)

    Article  ADS  Google Scholar 

  5. Kimble, H.J., Dagenais, M., Mandel, L.: Phys. Rev. Lett. 39, 691 (1977)

    Article  ADS  Google Scholar 

  6. Hillery, M., O’Connell, R.F., Scully, M.O., Wigner, E.P.: Phys. Rep. 106, 121–167 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  7. Kenfack, A., życzkowski, K.: J. Opt. B: Quantum Semiclass. Opt. 6, 396–404 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  8. Li, J., Li, G., Wang, J.M., Zhu, S.Y., Zhang, T.C.: J. Phys. B: At. Mol. Opt. Phys. 43, 085504 (2010)

    Article  ADS  Google Scholar 

  9. Hu, L.Y., Xu, X.X., Wang, Z.S., Xu, X.F.: Phys. Rev. A 82, 043842 (2010)

    Article  ADS  Google Scholar 

  10. Meng, X.G., Wang, Z., Fan, H.Y., Wang, J.S.: J. Opt. Soc. Am. B 29, 3141 (2012)

    Article  ADS  Google Scholar 

  11. Wang, Z., Li, H.M., Yuan, H.C.: J. Opt. Soc. Am. B 31, 2163 (2014)

    Article  ADS  Google Scholar 

  12. Agarwal, G.S., Tara, K.: Phys. Rev. A 43, 492 (1991)

    Article  ADS  Google Scholar 

  13. Xu, X.X., Hu, L.Y., Fan, H.Y.: Opt. Commun. 283, 1801 (2010)

    Article  ADS  Google Scholar 

  14. Hu, L.Y., Fan, H.Y.: J. Opt. Soc. Am. B 25, 1955 (2008)

    Article  ADS  Google Scholar 

  15. Sivakumar, S.: J. Phys. A: Math. Gen. 32, 3441 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  16. Duc, T.M., Noh, J.: Opt. Commun. 281, 2842 (2008)

    Article  ADS  Google Scholar 

  17. Zavatta, A., Viciani, S., Bellini, M.: Science 306, 660 (2004)

    Article  ADS  Google Scholar 

  18. Kalamidas, D., Gerry, C.C., Benmoussa, A.: Phys. Lett. A 372, 1937 (2008)

    Article  ADS  Google Scholar 

  19. García-Patrón, R., Eiurášek, J., Cerf, N.J., Wenger, J., Tualle-Brouri, R., Grangier, P.: Phys. Rev. Lett. 93, 130409 (2004)

    Article  ADS  Google Scholar 

  20. Park, J., Lee, S.Y., Lee, H.W., Nha, H.: J. Opt. Soc. Am. B 29, 906 (2012)

    Article  ADS  Google Scholar 

  21. Lee, S.Y., Ji, S.W., Lee, C.W.: Phys. Rev. A 87, 052321 (2013)

    Article  ADS  Google Scholar 

  22. Yang, Y., Li, F.L.: Phys. Rev. A 80, 022315 (2009)

    Article  ADS  Google Scholar 

  23. Kim, M.S.: J. Phys. B: At. Mol. Opt. Phys. 41, 133001 (2008)

    Article  ADS  Google Scholar 

  24. Parigi, V., Zavatta, A., Kim, M.S., Bellini, M.: Science 317, 1890 (2007)

    Article  ADS  Google Scholar 

  25. Yang, Y., Li, F.L.: J. Opt. Soc. Am. B 26, 830 (2009)

    Article  ADS  Google Scholar 

  26. Fiurášek, J.: Phys. Rev. A 80, 053822 (2009)

    Article  ADS  Google Scholar 

  27. Wang, Z., Yuan, H.C., Fan, H.Y.: J. Opt. Soc. Am. B 28, 1964 (2011)

    Article  ADS  Google Scholar 

  28. Lee, S.Y., Park, J., Ji, S.W., Ooi, C.H.R., Lee, H.W.: J. Opt. Soc. Am. B 26, 1532 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  29. Yuan, H.C., Xu, X.X., Fan, H.Y.: Sci. China Ser. G: Phys. Mech. Astron. 53, 1793–1798 (2010)

    Article  ADS  Google Scholar 

  30. Rennie, B.C., Dobson, A.J.: J. Comb. Theor. 7, 116 (1969)

    Article  MathSciNet  Google Scholar 

  31. Li, H.M., Yuan, H.C., Fan, H.Y.: Int. J. Theor. Phys. 48, 2849–2864 (2009)

    Article  MathSciNet  Google Scholar 

  32. Mehta, C.L.: Phys. Rev. Lett. 18, 752 (1967)

    Article  ADS  Google Scholar 

  33. Titulaer, U.M., Glauber, R.J.: Phys. Rev. 140, B676 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  34. Fan, H.Y., Zaidi, H.R.: Phys. Lett. A 124, 303 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  35. Wei, C.P., Xie, F.S., Zhang, H.L., Hu, L.Y.: Int. J Theor. Phys. 52, 798–810 (2013)

    Article  Google Scholar 

  36. Schleich, W.P.: Quantum Optics in Phase Space. Wiley, Berlin (2001)

    Book  MATH  Google Scholar 

  37. Genoni, M.G., Paris, M.G.A., Banaszek, K.: Phys. Rev. A 76, 042327 (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electrical and Optoelectronic Engineering, Changzhou Institute of Technology, Changzhou, 213002, China

    Jin Xiao, Chao Xiong, Hong-Chun Yuan, Lei Chen & Xi-Fang Zhu

  2. Changzhou Key Laboratory of Optoelectronic Materials and Devices, Changzhou, 213002, China

    Jin Xiao, Chao Xiong, Hong-Chun Yuan & Lei Chen

  3. Changzhou Institute of Modern Optoelectronic Technology, Changzhou, 213002, China

    Jin Xiao & Xi-Fang Zhu

Authors
  1. Jin Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chao Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong-Chun Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lei Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xi-Fang Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin Xiao.

Additional information

Supported by the National Natural Science Foundation of China (Nos.11447002, and 11447202) as well as the Research Foundation for Changzhou Institute of Modern Optoelectronic Technology (No.CZGY15)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiao, J., Xiong, C., Yuan, HC. et al. Non-positiveWigner Function and Non-Gaussianty Generated by Multiple Creation-then-annihilation Coherent State. Int J Theor Phys 55, 1719–1727 (2016). https://doi.org/10.1007/s10773-015-2812-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-015-2812-y

Keywords

Search

Navigation