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Dynamic properties of wehrl information entropy and wehrl phase distribution for a moving four-level atom

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Journal of Russian Laser Research Aims and scope

Abstract

We study the dynamics of the von Neumann entropy, Wehrl entropy, and Wehrl phase distribution for a single four-level ladder-type atom interacting with a one-mode cavity field taking into account the atomic motion. We obtain the exact solution of the model using the Schr¨odinger equation under specific initial conditions. Also we investigate the quantum and classical quantifiers of this system in the nonresonant case. We examine the effects of detuning and the atomic motion parameter on the entropies and their density operators. We observe an interesting monotonic relation between the different physical quantities in the case of nonmoving and moving atoms during the time evolution. We show that both the detuning and the atomic motion play important roles in the evolution of the Wehrl entropy, its marginal distributions, entanglement, and atomic populations.

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References

  1. E. T. Jaynes and F. W. Cummings, Proc. IEEE, 51, 89 (1963).

    Article  Google Scholar 

  2. M. Abdel-Aty, Physica A, 313, 471 (2001).

    Article  ADS  Google Scholar 

  3. T. M. El-Shahat, S. Abdel-Khalek, M. Abdel-Aty, and A.-S. F. Obada, Chaos, Solitons and Fractals, 18, 289 (2003).

  4. T. M. El-Shahat, S. Abdel-Khalek, and A.-S. F. Obada, Chaos, Solitons and Fractals, 26, 1293 (2005).

  5. Z. Liu, S. Zhu, and X-Shen Li, J. Mod. Opt., 35, 833 (1988).

  6. X.-S. Li, D. L. Lin, and C.-D. Gong, Phys. Rev. A, 36, 5209 (1987).

    Article  ADS  Google Scholar 

  7. Z.-D. Liu, X.-S. Li, and D. L. Lin, Phys. Rev. A, 36, 2205 (1987).

    Article  Google Scholar 

  8. C. V. Sukumar and B. Buck, J. Phys. A: Math. Gen., 17, 877 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  9. M. Janowicz and A. Orlowski, Rep. Math. Phys., 54, 57 (2004).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Y. Xue, G. Wang, J.-H. Wu, and J.-Y. Gao, Phys. Rev. A, 75, 063832 (2007).

    Article  ADS  Google Scholar 

  11. N. H. Abdel-Wahab, J. Phys. B: At. Mol. Opt. Phys., 41, 105502 (2008)

    Article  ADS  Google Scholar 

  12. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press (1955).

  13. K. Berrada, H. Eleuch, and Y. Hassouni, J. Phys. B: At. Mol. Opt. Phys., 44, 145503 (2011).

    Article  ADS  Google Scholar 

  14. K. Berrada, Opt. Commun., 285, 2227 (2012).

    Article  ADS  Google Scholar 

  15. K. Berrada and Y. Hassouni, Eur. Phys. J. D, 61, 513 (2011).

    Article  ADS  Google Scholar 

  16. K. Berrada, S. Abdel-Khalek, H. Eleuch, and Y. Hassouni, Quantum Inf. Process., [DOI 10.1007/s11128-011-0344-9].

  17. A. Wehrl, Rev. Mod. Phys., 50, 221 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  18. A. Wehrl, Rep. Math. Phys., 30, 119 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. A. Miranowicz, H. Matsueda, and M. R. B. Wahiddin, J. Phys. A: Math. Gen., 33, 5159 (2000).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. A. Anderson and J. J. Halliwell, Phys. Rev. D, 48, 2753 (1993).

    Article  MathSciNet  ADS  Google Scholar 

  21. A. Orlowski, H. Paul, and G. Kastelewicz, Phys. Rev. A, 52, 1621 (1995).

    Article  ADS  Google Scholar 

  22. A. Miranowicz, J. Bajer, M. R. B. Wahiddin, and N. Imoto, J. Phys. A: Math. Gen., 34, 3887 (2001).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. K. Piatek and W. Leonski, J. Phys. A: Math. Gen., 34, 4951 (2001).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. S. Abdel-Khalek and A.-S. F. Obada, Ann. Phys., 325, 2542 (2010).

    Article  ADS  MATH  Google Scholar 

  25. A.-S. F. Obada and S. Abdel-Khalek, J. Phys. A: Math. Gen., 37, 6573 (2004).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. S. Abdel-Khalek, Physica A, 387, 779 (2008).

    Article  ADS  Google Scholar 

  27. S. Abdel-Khalek, Phys. Scr., 80, 045302 (2009).

    Article  ADS  Google Scholar 

  28. S. Abdel-Khalek, S. Barzanjeh, and H. Eleuch, Int. J. Theor. Phys., 50, 2939 (2011).

    Article  MATH  Google Scholar 

  29. E. Schmidt, Math. Ann., 63, 433 (1906).

    Article  Google Scholar 

  30. C. H. Bennett, H. J. Berstein, S. Popescu, and B. Schumacher, Phys. Rev. A, 53, 2046 (1996).

    Article  ADS  Google Scholar 

  31. M. Abdel-Aty, Mod. Phys. Lett. B, 17, 253 (2003).

    Article  ADS  Google Scholar 

  32. X. Liu, Physica A, 286, 588 (2000).

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  34. S. Abdel-Khalek, K. Berreda, H. Eleuch, and M Abdel-Aty, Opt. Quantum Electron., 42, 887 (2011).

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science Taif University, Taif, Saudi Arabia

    S. Abdel-Khalek, A. A. Mousa & T. A. Nofal

  2. Mathematics Department, Faculty of Science Sohag University, Sohag, Egypt

    S. Abdel-Khalek

  3. Basic Science Department, Faculty of Engineering Menoufia University, Shebin El-Kom, Menoufia, Egypt

    A. A. Mousa

  4. Mathematics Department, Faculty of Science Minia University, Minia, Egypt

    T. A. Nofal

Authors
  1. S. Abdel-Khalek
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  2. A. A. Mousa
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  3. T. A. Nofal
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Correspondence to S. Abdel-Khalek.

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Abdel-Khalek, S., Mousa, A.A. & Nofal, T.A. Dynamic properties of wehrl information entropy and wehrl phase distribution for a moving four-level atom. J Russ Laser Res 33, 547–558 (2012). https://doi.org/10.1007/s10946-012-9314-7

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  • DOI: https://doi.org/10.1007/s10946-012-9314-7

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