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A tentative approach to entanglement measures for a system of a three-level atom interacting with a quantized cavity-field

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Abstract.

In this paper, an entanglement measure due to quasi-mutual entropy from initially entangled mixed states of a three-level atom interacting with a single cavity field is introduced. Detailed analytical and explicit expressions are given taking into account an arbitrary form of the intensity-dependent coupling. Despite its simplicity the model exhibits a very broad range of intricate physical effects and it is widely used in quantized theories of laser. We show that quantum revivals are possible for a broad continuous range of physical parameters in the case of initial coherent states. Entanglement degree effects are shown to be very sensitive to the initial state of the system. Numerical calculations under current experimental conditions are taken into account and it is found that the intensity-dependent coupling changes the general features dramatically.

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References

  1. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

  2. J. Eisert, M.B. Plenio, J. Mod. Opt. 46, 145 (1999)

    Article  Google Scholar 

  3. K.-H. Fichtner, M. Ohya, Commun. Math. Phys. 222, 229 (2001)

    MathSciNet  MATH  Google Scholar 

  4. M.A. Nielsen, J. Kempe, Phys. Rev. Lett. 86, 5184 (2001)

    Article  Google Scholar 

  5. C.H. Bennett , Phys. Rev. A 54, 3824 (1996)

    Article  MathSciNet  Google Scholar 

  6. S. Hill, W.K. Wootters, Phys. Rev. Lett. 78, 5022 (1997)

    Article  Google Scholar 

  7. V. Vedral, M.B. Plenio, Phys. Rev. A 57, 1619 (1998)

    Google Scholar 

  8. S. Furuichi, M. Ohya, Lett. Math. Phys. 49, 279 (1999)

    MathSciNet  MATH  Google Scholar 

  9. M. Abdel-Aty, S. Furuichi, A.-S.F. Obada, J. Opt. B: Quant. Semiclass. Opt. 4, 37 (2002)

    Article  Google Scholar 

  10. S. Scheel, J. Eisert, P.L. Knight, M.B. Plenio, J. Mod. Opt. 50, 881 (2003)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. S.J.D. Phoenix, P.L. Knight, Ann. Phys. (N.Y.) 186, 381 (1988)

    MATH  Google Scholar 

  13. S.J.D. Phoenix, P.L. Knight, Phys. Rev. A 44, 6023 (1991)

    Article  Google Scholar 

  14. M. Abdel-Aty, J. Phys. B: At. Mol. Opt. Phys. 33, 2665 (2000)

    Article  Google Scholar 

  15. M. Abdel-Aty, A.-S.F. Obada, Eur. Phys. J. D 23, 155 (2003)

    Google Scholar 

  16. M. Brune, J.M. Raimond, S. Haroche, Phys. Rev. A 35, 154 (1987)

    Google Scholar 

  17. L. Davidovich, J.M. Raimond, M. Brune, S. Haroche, Phys. Rev. A 36, 3771 (1987)

    Article  Google Scholar 

  18. P.A. Maia-Nieto, L. Davidovich, J.M. Raimond, Phys. Rev. A 43, 5073 (1991)

    Article  Google Scholar 

  19. J.M. Raimond , Rev. Mod. Phys. 73, 565 (2001)

    MathSciNet  Google Scholar 

  20. A. Messina, S. Maniscalco, A. Napoli, J. Mod. Opt. 50, 1 (2003)

    Google Scholar 

  21. A.M. Abdel-Hafez, A.-S.F. Obada, M.M.A. Ahmed, Physica A 144, 530 (1987)

    Article  Google Scholar 

  22. A.M. Abdel-Hafez, A.M.M. Abu-Sitta, A.-S.F. Obada, Physica A 156, 689 (1989)

    MathSciNet  Google Scholar 

  23. A. Ekert, P.L. Knight, Am. J. Phys. 63, 415 (1994)

    Google Scholar 

  24. S.B. Zheng, Quant. Semiclass. Opt. B 10, 691 (1998)

    Article  Google Scholar 

  25. N.J. Cerf, M. Bourennane, A. Karlsson, N. Gisin, Phys. Rev. Lett. 88, 127902 (2002)

    Article  Google Scholar 

  26. M. Bourennane, A. Karlsson, G. Bjork, Phys. Rev. A 64, 012306 (2001)

    Article  Google Scholar 

  27. D. Bruss, C. Macchiavello, Phys. Rev. Lett. 88, 127901 (2002)

    Article  Google Scholar 

  28. T. Durt, N.J. Cerf, N. Gisin, M. Zukowski, quant-ph/0207057.

  29. A. Acin, T. Durt, N. Gisin, J.I. Latorre, Phys. Rev. A 65, 052325 (2002)

    Article  Google Scholar 

  30. D. Kaszlikowski, P. Gnascinski, M. Zukowski, W. Miklaszewski, A. Zeilinger, Phys. Rev. Lett. 85, 4418 (2000)

    Article  Google Scholar 

  31. J.M. Raimond , Rev. Mod. Phys. 73, 565 (2001)

    MathSciNet  Google Scholar 

  32. M. Ikram, F. Saif, Phys. Rev. A 67, 069901(E) (2003)

    Article  Google Scholar 

  33. A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001)

    Article  Google Scholar 

  34. A. Lamas-Linares , Nature 412, 887 (2001)

    Article  Google Scholar 

  35. J.C. Howell , Phys. Rev. Lett. 88, 030401 (2002)

    Article  Google Scholar 

  36. H. Araki, E. Lieb, Commun. Math. Phys. 18, 160 (1970)

    Google Scholar 

  37. A.G. White, D.F.V. James, P.H. Eberhard, P.G. Kwiat, Phys. Rev. Lett. 83, 3103 (1999)

    Article  Google Scholar 

  38. D.F.V. James, P.G. Kwiat, W.J. Munro, A.G. White, Phys. Rev. A 64, 052312 (2001)

    Article  Google Scholar 

  39. K. Audenaert, M.B. Plenio, J. Eisert, Phys. Rev. Lett. 90, 027901 (2003)

    Article  Google Scholar 

  40. M. Ohya, Rep. Math. Phys. 27, 19 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  41. O. Benson, G. Raithel, H. Walther, Phys. Rev. Lett. 72, 3506 (1994)

    Article  Google Scholar 

  42. Dynamics of the micromaser field in electron theory and quantum electrodynamics: 100 years later, edited by J.P. Dowling (Plenum Press, New York, 1997)

  43. C.C. Gerry, J.H. Eberly, Phys. Rev. A 42, 6805 (1990)

    Article  Google Scholar 

  44. M. Abdel-Aty, Rep. Math. Phys. (2003, preprint)

  45. S. Virmani, M.B. Plenio, Phys. Lett. A 268, 31 (2000)

    MathSciNet  MATH  Google Scholar 

  46. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

    Article  Google Scholar 

  47. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)

    MathSciNet  MATH  Google Scholar 

  48. M. Brune, E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wunderlich, J.M. Raimond, S. Haroche, Phys. Rev. Lett. 77, 4887 (1996)

    Article  Google Scholar 

  49. L. Davidovich, N. Zagury, M. Brune, J.M. Raimond, S. Haroche, Phys. Rev. A 50, R895 (1994)

  50. A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J.M. Raimond, S. Haroche, e-print arXiv: quantum-ph/0105062

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt

    Abdel-Shafy F. Obada

  2. Mathematics Department, Faculty of Science, South Valley University, 82524, Sohag, Egypt

    Mahmoud Abdel-Aty

Authors
  1. Abdel-Shafy F. Obada
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  2. Mahmoud Abdel-Aty
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Correspondence to Mahmoud Abdel-Aty.

Additional information

Received: 2 June 2003, Published online: 26 August 2003

PACS:

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell’s inequalities, GHZ states, etc.) - 03.67.Hk Quantum communication - 42.65.-k Nonlinear optics - 32.80.Rm Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)

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Obada, AS.F., Abdel-Aty, M. A tentative approach to entanglement measures for a system of a three-level atom interacting with a quantized cavity-field. Eur. Phys. J. D 27, 277–285 (2003). https://doi.org/10.1140/epjd/e2003-00267-5

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  • DOI: https://doi.org/10.1140/epjd/e2003-00267-5

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