Skip to main content
SpringerLink
Log in

Quantum Treatment of the Interaction Between an N-Level Atom and Two Noninteracting Two-Level Atoms

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We consider the problem of two two-level atoms interacting with N-level atom. We obtain the exact solution for the wave function for the case where both atoms are identical and the system is treated at exact resonance. We use the results obtained for discussing the temporal evolution of the atomic inversion, in particular, the collapse and revival phenomena. We build up our discussion on the variation of the atomic number j and the atomic angle θ. For small j, the system exhibits a small period of collapse, and for large j we observe a long period of revival. We employ the linear entropy in the discussion of entanglement. We show that the atomic angle θ influences the system in such a way that the period of partial entanglement increases with increase in the value of θ. In addition to the variance squeezing, we also examine the entanglement between the spinors and show that the squeezing phenomenon occurs in the second quadrature, being absent in the first quadrature. Also we realize that the squeezing phenomenon reaches its maximum and gets more pronounced for a small value of the atomic number and a large value of the atomic angle.

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

Similar content being viewed by others

References

  1. S. S. Hassan, M. S. Abdalla, A.-S. F. Obada, and H. A. Batarfi, J. Mod. Opt., 40, 1351 (1993).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. M. S. Abdalla, S. S. Hassan, and A.-S. F. Obada, Phys. Rev. A, 34, 4869 (1986).

    Article  ADS  Google Scholar 

  3. M. S. Abdalla, M. M. A. Ahmed, and S. Al-Homidan, J. Phys. A: Math. Gen., 31, 3117 (1998).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. M. S. Abdalla, Int. J. Mod. Phys. B, 16, 2837 (2002).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. M. S. Abdalla, J. Peˇrina, and J. Kˇrepelka, J. Opt. Soc. Am. B, 23, 1146 (2006).

    Article  MathSciNet  ADS  Google Scholar 

  6. M. S. Abdalla and M. M. Nassar, Ann. Phys. N.Y., 324, 637 (2009).

    Article  MATH  ADS  Google Scholar 

  7. M. S. Abdalla, J. Peˇrina, and J. Kˇrepelka, Opt. Commun., 282, 2878 (2009).

    Article  ADS  Google Scholar 

  8. M. Tavis and F. W. Cummings, Phys. Rev., 170, 379 (1968).

    Article  ADS  Google Scholar 

  9. M. Tavis and F. W. Cummings, Phys. Rev., 188, 692 (1969).

    Article  ADS  Google Scholar 

  10. E. M. Khalil, M. S. Abdalla, A.-S. F. Obada, and J. Peˇrina, J. Opt. Soc. Am. B, 37, 266 (2010).

    Article  ADS  Google Scholar 

  11. M. S. Abdalla, E. M. Khalil, and A.-S. F. Obada, Ann. Phys. N.Y., 322, 2554 (2007).

    Article  MATH  ADS  Google Scholar 

  12. E. M. Khalil, M. S. Abdalla, and A.-S. F. Obada, Ann. Phys. N.Y., 321, 421 (2006).

    Article  MATH  ADS  Google Scholar 

  13. E. M. Khalil, M. S. Abdalla, and A.-S. F. Obada, J. Phys. B: At. Mol. Opt. Phys., 43, 0955078 (2010).

    Article  Google Scholar 

  14. M. S. Abdalla, A.-S. F. Obada, and M. Abdel-Aty, Ann. Phys. N.Y., 318, 266 (2005).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. M. S. Abdalla, J. Kˇrepelka, and J. Peˇrina, J. Phys. B: At. Mol. Opt. Phys., 39, 1563 (2006).

    Article  ADS  Google Scholar 

  16. M. S. Abdalla, H. Elech, and J. Peˇrina, J. Opt. Soc. Am. B, 29, 719 (2012).

    Article  ADS  Google Scholar 

  17. M. S. Abdalla, E. M. Khalil, and A.-S. F. Obada, Ann. Phys. N.Y., 326, 2486 (2011).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. E. M. Khalil and M. S. Abdalla, J. Russ. Laser Res., 33, 128 (2012).

    Article  Google Scholar 

  19. M. S. Abdalla and E. M. Khalil, J. Russ. Laser Res., 33, 328 (2012).

    Article  Google Scholar 

  20. M. G. Benedict, Superradiance, Taylor & Frances Group (1996).

  21. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, Wiley (1975).

  22. M. Sargent, M. O. Scully, and W. E. Lamb Jr., Laser Phys., Addison-Wesley (1974).

  23. A. Wallraff, D. I. Schuster, A. Blais, et al., Lett. Nature, 431, 162 (2004).

    Article  ADS  Google Scholar 

  24. M. S. Abdalla, E. Lashin, and G. Sadiek, J. Phys. B: At. Mol. Opt. Phys., 41, 015502 (2008).

    Article  ADS  Google Scholar 

  25. G. Sadiek, E. Lashin, and M. S. Abdalla, Physica B, 404,1719 (2009).

    Article  ADS  Google Scholar 

  26. F. A. A. El-Orany and M. S. Abdalla, J. Phys. A: Math. Theor., 44, 035302 (2011).

    Article  MathSciNet  ADS  Google Scholar 

  27. Heinz-Peter Breuer, D. Burgarth, and F. Petruccione, Phys. Rev. B, 70, 045323 (2004).

    Article  ADS  Google Scholar 

  28. Y. Hamdouni and F. Petruccione, Phys. Rev. B, 76, 174306 (2007).

    Article  ADS  Google Scholar 

  29. M. S. Abdalla, M. M. A. Ahmed, and A.-S. F.Obada, J. Russ. Laser Res., 34, 87 (2013).

    Article  Google Scholar 

  30. J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys., 73, 565 (2001).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. D. N. Matsukevich, T. Chanelire, S. D. Jenkins, et al., Phys. Rev. Lett., 96, 030405 (2006).

    Article  ADS  Google Scholar 

  32. P. Masiak, Phys. Rev. A, 66, 023804 (2002).

    Article  ADS  Google Scholar 

  33. A. Datta, B. Ghosh, A. S. Majumdar, and N. Nayak, Europhys. Lett., 67, 934 (2004).

    Article  ADS  Google Scholar 

  34. M. S. Kim, Jinhyoung Lee, D. Ahn, and P. L. Knight, Phys. Rev. A, 65, 040101(R) (2002).

    Article  ADS  Google Scholar 

  35. T. Tessier, A. Delgado, I. Fuentes-Guridi, and I. H. Deutsch, Phys. Rev. A ,68, 062316 (2003).

    Article  ADS  Google Scholar 

  36. S. Bose, I. Fruentes-Guridi, P. L. Knight, and V. Vedral, Phys. Rev. Lett., 87, 050401 (2001).

    Article  MathSciNet  ADS  Google Scholar 

  37. E. M. Khalil, M. S. Abdalla, A.-S.F. Obada, and J. Peˇrrina, J. Opt. Soc. Am. B, 27, 266 (2010).

    Article  ADS  Google Scholar 

  38. E. M. Khalil, M. S. Abdalla, and A. S.-F. Obada, J. Phys. B: At. Mol. Opt. Phys., 43, 095507 (2010).

    Article  ADS  Google Scholar 

  39. L. Zhou, X. X. Yi, H. S. Song, and Y. Q. Quo, J. Opt. B: Quantum Semiclass. Opt., 6, 378 (2004).

    Article  ADS  Google Scholar 

  40. L. Zhou, H. S. Song, and C. Li, J. Opt. B: Quantum Semiclass. Opt., 4, 425 (2002).

    Article  ADS  Google Scholar 

  41. C. C. Gerry and P. L. Knight, Introductory Quantum Optics, Cambridge University Press (2005), p. 108.

  42. F. A. A. El-Orany, J. Mod. Opt., 56, 99 (2009).

    Article  MATH  Google Scholar 

  43. S. Choi and N. P. Bigelow, Phys. Rev. A, 72, 033612 (2005).

    Article  ADS  Google Scholar 

  44. A. Sorensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature, 409, 63 (2001).

    Article  ADS  Google Scholar 

  45. Mao-Fa Fang, Peng Zhou, and S. Swain, J. Mod. Opt., 47, 1043 (2000).

    Article  MATH  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    M. Sebawe Abdalla

  2. Mathematics Department, Faculty of Science, Al-Azher University, Nassr City, 11884, Cairo, Egypt

    M. M. A. Ahmed, E. M. Khalil & A. S.-F. Obada

Authors
  1. M. Sebawe Abdalla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. A. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. M. Khalil
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. S.-F. Obada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Sebawe Abdalla.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdalla, M.S., Ahmed, M.M.A., Khalil, E.M. et al. Quantum Treatment of the Interaction Between an N-Level Atom and Two Noninteracting Two-Level Atoms. J Russ Laser Res 35, 169–181 (2014). https://doi.org/10.1007/s10946-014-9411-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-014-9411-x

Keywords

Search

Navigation