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International Journal of Theoretical Physics

, Volume 57, Issue 9, pp 2615–2627 | Cite as

Entangled Two Two-Level Atom in the Presence of External Classical Fields

  • E. M. Khalil
  • S. Abedel-Khalek
Article
  • 37 Downloads

Abstract

In this contribution, we investigate a TTLAs (two two-level atoms) in interaction with an electromagnetic field in presence of the external classical fields. The general solution of the time evolution operator is obtained and used to derive the density matrix operator. The temporal evolution of the atomic inversion, the degree of entanglement measured by the negativity, as well as the single atom entropy squeezing are discussed. We consider the atomic system at either the upper or Bell states, while the field in the coherent state. It has been shown that the coupling parameter g (the coupling of the external classical fields) gets more effective for the case in which the g is not equal to zero. Also for a strong coupling parameter g the superstructure phenomenon can be reported. The results shown that for increase the value of the classical external fields parameter leads to the entanglement between the atoms and the fields gets stronger. Also it has shown that for specific value of the classical external fields the system never reaches the pure state except during the revival periods.

Keywords

External classical fields Entropy squeezing Entanglement Negativity 

Notes

Acknowledgments

The authors would like to thank the deanship of scientific research at Taif University to support this research (no.1-438-5752) and encourage researchers to continue the scientific research.

References

  1. 1.
    Jaynes, E.T., Cummings, F.W.: Proc. IEEE 51, 89 (1963)CrossRefGoogle Scholar
  2. 2.
    Obada, A.-S. F., Khalil, E.M.: Int. J. Theo. Phys. 49, 1823 (2010)CrossRefGoogle Scholar
  3. 3.
    Algarni, A., Abdel-Khalek, S.: Appl. Math. Inf. Sci. 10, 657 (2016)CrossRefGoogle Scholar
  4. 4.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambrige University Press, Cambrige (2000)MATHGoogle Scholar
  5. 5.
    Bouwmeester, D., Ekert, A., Zeilinger, A. (eds.): The Physics of Quantum Information. Springer, Berlin (2000)Google Scholar
  6. 6.
    von Neumann, J.: The Measuring Process in Mathematische Grundlagen Der Quantenmechanik, Ch. 5. Springer, Berlin (1932)Google Scholar
  7. 7.
    Berrada, K., Chafik, A., Eleuch, H., Hassouni, Y.: Quantum Inf. Process. 9(1), 13 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Sete, E.A., Svidzinsky, A.A., Rostovtsev, Y.V., Eleuch, H., Jha, P.K., Suckewer, S., Scully, M.O.: IEEE J. Sel. Top. Quantum Electron. 18, 541 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Eleuch, H.: Euro. Phys. J. D 49(3), 391 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Eleuch, H., Nessib, N.B., Bennaceur, R.: Euro. Phys. J. D 29, 391 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    Sete, E.A., Eleuch, H.: Phys. Rev. A 89, 013841 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    Jabri, H., Eleuch, H., Djerad, T.: Laser Phys. Lett. 2, 253 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    Eleuch, H., Courty, J.M., Messin, G., Fabre, C., Giacobino, E.: J. Opt. B 1, 1 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    Khalil, E.M., Abdalla, M.S., Obada, A.-S. F., Perina, J.: J. Opt. Soc. Am. B 27, 266 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    Khalil, E.M., Abdalla, M.S., Obada, A.-S.F.: J. Phys. B 43(9), 095507 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    Obada, A.-S.F., Abdalla, M.S., Khalil, E.M.: Physica A 336, 433 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    Abdalla, M.S., Khalil, E.M., Obada, A.-S. F.: Physica A 454, 99 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    Abdalla, M.S., Khalil, E.M., Obada, A.-S.F., Perina, J., Repelka, J.K.: Am. Inst. Phys. (AIP) 7(1), 015013 (2017)Google Scholar
  19. 19.
    Obada, A.-S. F., Abdalla, M.S., Khalil, E.M.: Int. J. Theo. Phys. 42, 2735 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    Khalil, E.M., Abdalla, M.S., Obada, A.-S. F.: Int. J. Mod. Phys. B 18 (16), 2325 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    Abdalla, M.S., Khalil, E.M., Ali, S.I.: J. Russian Laser Res. 35(4), 408 (2014)CrossRefGoogle Scholar
  22. 22.
    Obada, A.-S. F., Abdel-Khalek, S., Abo-Kahla, D.A.M.: Opt. Commun. 283, 4662 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    Abdel-Khalek, S., Halawani, S.H.A., Obada, A.-S. F.: Int. J. Theo. Phys. 56, 2898 (2017)CrossRefGoogle Scholar
  24. 24.
    Alqannas, H.S., Khalil, E.M.: Int. J. Theo. Phys. 56, 2019 (2017)CrossRefGoogle Scholar
  25. 25.
    Abu-Zinadah, H.H., Abdel-Khalek, S.: Results Phys. 7, 4318 (2017)ADSCrossRefGoogle Scholar
  26. 26.
    Abdalla, M.S., Ahmed, M.M.A., Khalil, E.M., Obada, A.-S. F.: Ann. Phys. 364, 168 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    Phoenix, S.J.D., Knight, P.L.: Phys. Rev. A 44, 6023 (1991)ADSCrossRefGoogle Scholar
  28. 28.
    Phoenix, S.J.D., Knight, P.L.: Phys. Rev. Lett. 66, 2833 (1991)ADSCrossRefGoogle Scholar
  29. 29.
    Breuer, H.P., Petruccione, F.: Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)MATHGoogle Scholar
  30. 30.
    Carmichael, H.: An Open Systems Approach to Quantum Optics. Springer, Berlin (1993)MATHGoogle Scholar
  31. 31.
    Abdalla, M.S., Khalil, E.M., Obada, A.-S. F.: Int. J. M. Phys. B 31, 1750211 (2017)ADSCrossRefGoogle Scholar
  32. 32.
    Vidal, G., Werner, R.F.: Phys. Rev. A 65, 032314 (2002)ADSCrossRefGoogle Scholar
  33. 33.
    Berrada, K., Abdel-Khalek, S., Obada, A.-S. F.: Phys. Lett. A 376, 1412 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    Sanchez-Ruiz, J.: Phys. Lett. A 201, 125 (1995)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Sanchez-Ruiz, J.: Phys. Lett. A 244, 189 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    Obada, A.-S. F., Khalil, E.M., El-Deberky, M.A., Sanad, S.: Quant. Inf. Rev. 3(1), 9 (2015)Google Scholar
  37. 37.
    Abdalla, M.S., Obada, A.-S. F., Khalil, E.M., Ahmed, M.M.A.: J. Russ. Laser Res. 36(2), 119 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceTaif UniversityTaifSaudi Arabia
  2. 2.Mathematics Department, Faculty of ScienceAl-Azher UniversityNassr CityEgypt
  3. 3.Mathematics Department, Faculty of ScienceSohag UniversitySohagEgypt

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