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Entangled Pair of the su(1) Quantum Systems Interacting with Two Two-Level Atoms

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Journal of Russian Laser Research Aims and scope

Abstract

In this communication, we consider a pair of entangled quantum systems, each described by the su(1) Lie algebra, interacting with two two-level atoms. We discuss in detail the influence of the detuning terms on the system and derive from the Heisenberg equations of motion the expressions of various operators corresponding to the dynamics. Solving the associated Schrödinger equation, we obtain the general solution. Then we calculate and discuss in detail the expression of the von Neumann entropy for the two qubits and the radiation field. We examine the negativity index to gauge the degree of quantum entanglement between the su(1) quantum system and the atoms. Finally, we compare the results of the negativity and von Neumann entropy for some values of the initial state and the detuning parameter.

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References

  1. J. A. Wheeler and W. H. Zurek. Quantum Theory and Measurement, Princeton University Press, NJ (1983).

    Book  Google Scholar 

  2. W. K. Wootters, Quantum Inform. Comput., 1, 27 (2001).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  4. S. Popescu and D. Rohrlich, Phys. Rev. A, 56, R3319 (1997).

    Article  ADS  Google Scholar 

  5. M. A. Nielsen, Phys. Rev. Lett., 83, 436 (1999).

    Article  ADS  Google Scholar 

  6. R. F. Werner, Phys. Rev. A, 40, 4277 (1989).

    Article  ADS  Google Scholar 

  7. W. H. \( \tilde{\mathrm{Z}} \)urek, Phys. Today, 44, 36 (1991).

  8. A. O. Caldeira and A. J. Leggett, Physica A, 121, 587 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  9. R. Omnès, The Interpretation of Quantum Mechanics, Princeton University Press, NJ (1994).

    Book  Google Scholar 

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

  11. M. A. Man’ko and V. I. Man’ko, I. J. Quantum Inf., 12, 1560006 (2014).

    Article  Google Scholar 

  12. V. A. Andreev, V. I. Man’ko, O. V. Man’ko, and E. V. Shchukin, Theor. Math. Phys., 146, 140 (2006).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. A. Vaglica and G. Vetric, Phys. Rev. A, 75, 062120 (2007).

  15. A. F. Al Naim, J. Y. Khan, S. Abdel-Khalek, and E. M. Khalil, J. Russ. Laser Res., 39, 505 (2018).

    Article  Google Scholar 

  16. S. Abdel-Khalek, S. H. A. Halawani, and A.-S. F. Obada, Int. J. Theor. Phys., 56, 2898 (2017).

    Article  Google Scholar 

  17. N. N. Bogoliubov and N. N. Bogolyubov, Jr., Aspects of Polaron Theory. Equilibrium and Nonequilibrium, World Scientific, Singapore (2008).

    Book  Google Scholar 

  18. N. N. Bogolyubov, Jr., M. Yu. Rasulova, and I. A. Tishabaev, Theor. Math. Phys., 171, 523 (2012).

    Article  Google Scholar 

  19. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information, Springer, Berlin (2000).

    Book  Google Scholar 

  20. C. H. Bennett, G. Brassard, C. Crepeau, et al., Phys. Rev. Lett., 70, 1895 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  21. C. H. Bennett and S. J. Wiesner, Phys. Rev. Lett., 69, 2881 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  22. C. A. Fuchs, N. Gisin, R. B. Griffiths, et al., Phys. Rev. A, 56, 1163 (1997).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  28. 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 

  29. S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A, 57, 822 (1998).

    Article  ADS  Google Scholar 

  30. E. M. Khalil, Int. J. Mod. Phys. B, 30, 5143 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  31. M. Sebawe Abdalla, E. M. Khalil, and A.-S. F. Obada, Ann. Phys., 11, 2554 (2007).

    Article  Google Scholar 

  32. E. M. Khalil, M. Sebawe Abdalla, and A.-S. F. Obada, Ann. Phys., 321, 421 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. S. J. D. Phoenix and P. L. Knight, Phys. Rev. Lett., 66, 2833 (1991).

    Article  ADS  Google Scholar 

  35. M. Abdel-Aty, S. Abdel-Khalek, and A.-S. F. Obada, Chaos, Solitons, Fractals, 12, 2015 (2001).

    Article  Google Scholar 

  36. S. Abdel-Khalek, App. Math. Inform. Sci., 1, 53 (2007).

    MathSciNet  Google Scholar 

  37. A.-S. F. Obada, S. Abdel-Khalek, and D. A. M. Abo-Kahla, Opt. Commun., 283, 4662 (2010).

    Article  ADS  Google Scholar 

  38. S. Abdel-Khalek, Open Sys. Inform. Dyn., 22, 1550015 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  39. A.-S. F. Obada, A. F. Al Naim, E. M. Khalil, et al., Opt. Quantum Electron., 51, 259 (2019).

    Article  Google Scholar 

  40. A.-S. F. Obada, M. M. A. Ahmed, F. K. Faramawy, and E. M. Khalil, Chaos, Solitons, Fractals, 28, 983 (2006).

    Article  Google Scholar 

  41. H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2002).

  42. H. Carmichael, An Open Systems Approach to Quantum Optics, Springer, Berlin (1993).

    Book  Google Scholar 

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Authors and Affiliations

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

    S. Abdel-Khalek, E. M. Khalil & Beida Alsubei

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

    S. Abdel-Khalek

  3. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt

    E. M. Khalil

  4. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    N. N. Bogolubov Jr

  5. Institute of Nuclear Physics, Academy of Sciences of Uzbekistan, Ulughbek, Tashkent, Uzbekistan, 100214

    M. Yu. Rasulova

Authors
  1. S. Abdel-Khalek
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  2. E. M. Khalil
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  3. Beida Alsubei
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  4. N. N. Bogolubov Jr
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  5. M. Yu. Rasulova
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Correspondence to S. Abdel-Khalek.

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Abdel-Khalek, S., Khalil, E.M., Alsubei, B. et al. Entangled Pair of the su(1) Quantum Systems Interacting with Two Two-Level Atoms. J Russ Laser Res 41, 30–39 (2020). https://doi.org/10.1007/s10946-020-09854-0

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  • DOI: https://doi.org/10.1007/s10946-020-09854-0

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