Some features of the geometric phase and entanglement of three-level atom under cavity damping effects

  • S. Abdel-KhalekEmail author
  • Y. S. El-Saman
  • I. Mechai
  • M. Abdel-Aty
Original Paper


In this manuscript, we present a system consisting of a three-level atom interacting with optical field. We investigate qualitatively the entanglement and atomic (field) geometric phase under the effect of cavity damping. The atom–field entanglement is measured by the negativity. We show that these quantifiers depend strongly on the variations of the initial settings of the atom, and this exhibits substantial phenomena that depend on the cavity damping effect. Finally, we explore the link between the entanglement and atomic (field) geometric phase of different physical parameters within the presence and absence of the cavity damping effect.


Entanglement Geometric phase Cavity damping Negativity 


03.67.Bg 42.50.Dv 42.50.Pq 



  1. [1]
    W Zurek Rev. Mod. Phys.75 715 (2001)ADSCrossRefGoogle Scholar
  2. [2]
    A-B A Mohamed and H Eleuch Eur. Phys. J. Plus132 75 (2017)CrossRefGoogle Scholar
  3. [3]
    C H Bennett and D P Divincenzo Nature404 247 (2000)ADSCrossRefGoogle Scholar
  4. [4]
    I Bengtsson and K Zyczkowski (Cambridge: Cambridge University Press) (2006)Google Scholar
  5. [5]
    C H Bennett, G Brassard, R Jozsa, A Peres and W K Wootters Phys. Rev. Lett.70 1895 (1993)ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    X Y Li, Q Pan, J Jing, J Zhang, C Xie and K Peng Phys. Rev. Lett.88 047904 (2002)ADSCrossRefGoogle Scholar
  7. [7]
    T M El-shahat, S Abdel-khalek, M Abdel-Aty and A S F Obada J. Mod. Opt.50 2013 (2003)ADSCrossRefGoogle Scholar
  8. [8]
    M Murao, D Jonathan, M B Plenio and V Vedral Phys. Rev. A59 156 (1999)ADSCrossRefGoogle Scholar
  9. [9]
    A Miranowicz, P Horodecki, R W Chhajlany, J Tuziemski and J Sperling Phys. Rev. A86 042123 (2012)ADSCrossRefGoogle Scholar
  10. [10]
    J K Kalaga, W Leoński and J Peřina Jr Phys. Rev. A97 042110 (2018)ADSCrossRefGoogle Scholar
  11. [11]
    H-Y Ku, S-L Chen, C Budroni, A Miranowicz, Y-N Chen and F Nori Phys. Rev. A97 022338 (2018)ADSCrossRefGoogle Scholar
  12. [12]
    J K Kalaga and W Leonski Quantum Inf. Process16 175 (2017)ADSCrossRefGoogle Scholar
  13. [13]
    J K Kalaga, W Leonski and R Szczesniak Quantum Inf. Process16 265 (2017)ADSCrossRefGoogle Scholar
  14. [14]
    J C Garrison and E M Wright Phys. Lett. A128 177 (1988)ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    G Dattoli, R Mignani and A Torre J. Phys. A23 5795 (1990)ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    A Kvitsinsky and S Putterman J. Math. Phys.32 1403 (1991)ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    J Anandan, J Christian and K Wanelik Am. J. Phys.65 180 (1997)ADSCrossRefGoogle Scholar
  18. [18]
    A G Wagh et al Phys. Rev. Lett.78 755 (1997)ADSCrossRefGoogle Scholar
  19. [19]
    M Abdel-Aty J. Phys. A41 185304 (2008)MathSciNetCrossRefGoogle Scholar
  20. [20]
    C L Webb et al Phys. Rev. A60 R1783 (1999)ADSCrossRefGoogle Scholar
  21. [21]
    S Abdel-Khalek, K Berrada, H Eleuch and M Abel-Aty Opt. Quantum Electron.42 887 (2011)CrossRefGoogle Scholar
  22. [22]
    M Abdel-Aty Eur. Phys. J. D46 537 (2008)ADSCrossRefGoogle Scholar
  23. [23]
    T M El-Shahat, S Abdel-Khalek and A S-F Obada Chaos Solitons Fractals26 1293 (2005)ADSCrossRefGoogle Scholar
  24. [24]
    S Abdel-Khalek and A M Ahmed Appl. Math. Inf. Sci.5 263S (2011)Google Scholar
  25. [25]
    R Dermez and S Abdel-Khalek J. Russ. Laser Res.32 287 (2008)CrossRefGoogle Scholar
  26. [26]
    M V Berry Proc. R. Soc. A45 392 (1984)Google Scholar
  27. [27]
    F Gaitan Phys. Rev. A58 1665 (1998)ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    D Ellinas, S M Barnett and M A Dupertuis Phys. Rev. A39 3228 (1989)ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    D Gamliel and J H Freed Phys. Rev. A39 3238 (1989)ADSCrossRefGoogle Scholar
  30. [30]
    S Abdel-Khalek Open Syst. Inf. Dyn.22 1550015 (2015)MathSciNetCrossRefGoogle Scholar
  31. [31]
    B M Villegas-Martinez, F Soto-Eguibar and H M Moya-Cessa Adv. Math. Phys.2016 7926509 (2016)CrossRefGoogle Scholar
  32. [32]
    A Rivas, A D Kapto, S F Huelega and M B Plenio New J. Phys.12 113032 (2010)ADSCrossRefGoogle Scholar
  33. [33]
    S Abdel-Khalek and A S-F Obada Ann. Phys.325 2542 (2010)ADSCrossRefGoogle Scholar
  34. [34]
    D Markham, M Murao and V Vedral Phys. Rev. A70 062312 (2003)ADSCrossRefGoogle Scholar
  35. [35]
    A-S F Obada, S Abdel-Khalek, K Berrada and M E Shaheen Physica A392 6642 (2013)CrossRefGoogle Scholar
  36. [36]
    Y Aharonov and J Anandan Phys. Rev. Lett.58 1593 (1987)ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    D P Datta Phys. Rev. D48 5746 (1993)ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    A-S F Obada and A-B Mohamed Ann. Phys.326 2369 (2011)ADSCrossRefGoogle Scholar
  39. [39]
    M Abdel-Aty J. Phys. A38 8589 (2005)ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    M Abdel-Aty J. Mod. Opt.50 161 (2003)ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    M Abdel-Aty J. Math. Phys.44 1457 (2003)ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    D M Tong, E Sjqvist, L Kwek and C H Oh Phys. Rev. Lett.93 080405 (2004)ADSCrossRefGoogle Scholar
  43. [43]
    S Abdel-Khalek, Y S El-Saman, I Mechai and M Abdel-Aty Braz. J. Phys.48 9 (2018)ADSCrossRefGoogle Scholar
  44. [44]
    J K Kalaga, A Kowalewska-Kudłaszyk, W Leoński and A Barasiński Phys. Rev. A94 032304 (2016)ADSCrossRefGoogle Scholar
  45. [45]
    E Schrodinger Math. Proc. Camb. Philos. Soc.31 555 (1935)ADSCrossRefGoogle Scholar
  46. [46]
    T Liu, J Wang, J Jing and H Fan Ann. Phys.390 334 (2018)ADSCrossRefGoogle Scholar
  47. [47]
    K Bartkiewicz, A Cernoch, K Lemr, A Miranowicz and F Nori Sci. Rep.6 38076 (2016)ADSCrossRefGoogle Scholar
  48. [48]
    S-L Chen, N Lambert, C-M Li, G-Y Chen, Y-N Chen, A Miranowicz and F Nori Sci. Rep.7 3728 (2017)ADSCrossRefGoogle Scholar
  49. [49]
    H M Wiseman, S J Jones and A C Doherty Phys. Rev. Lett.98 140402 (2007)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  • S. Abdel-Khalek
    • 1
    • 2
    Email author
  • Y. S. El-Saman
    • 3
  • I. Mechai
    • 3
  • M. Abdel-Aty
    • 2
    • 4
  1. 1.Department of Mathematics, Faculty of ScienceTaif UniversityTaifSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceSohag UniversitySohagEgypt
  3. 3.Department of Mathematics, Faculty of ScienceJazan UniversityJazanSaudi Arabia
  4. 4.Institute of Basic and Applied SciencesEgypt-Japan University, E-JUSTAlexandriaEgypt

Personalised recommendations