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Effect of an External Magnetic Field on Some Statistical Properties of the 2+1 Dirac–Moshinsky Oscillator

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Journal of Russian Laser Research Aims and scope

Abstract

We map the 2+1 Dirac–Moshinsky oscillator (2+1 DMO) into the generalized Jaynes–Cummings model (GJCM), where an external magnetic field is coupled to an external isospin field. We solve analytically the basic equations of the model, where the coherent state is considered as an initial state. The results obtained show that the magnetic field strength and the coupling parameter of the isospin field play important roles when some statistical properties such as the entanglement, population inversion, and degree of coherence are considered. We show that these parameters are important for increasing the entanglement and also demonstrate the collapse and revival phenomena.

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References

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

    Article  Google Scholar 

  2. S. Haroche and J. M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons, Oxford University Press (2007).

  3. J. H. Eberly, N. B. Narozhny, and J. J. S.-Mondragon, Phys. Rev. Lett., 44, 1323 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  4. N. B. Narozhny, J. J. S. -Mondragon, and J. H. Eberly, Phys. Rev. A, 23, 236 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  5. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010).

  6. D. Ito, K. Mori, and E. Carrieri, Nuovo Cimento A, 51, 119 (1967).

    Article  Google Scholar 

  7. P. A. Cook, Lett. Al Nuovo Cimento, 1, 419 (1971).

    Article  Google Scholar 

  8. M. Moshinsky and A. Szczepaniak, J. Phys. A: Math. Gen., 22, 817 (1989).

    Article  ADS  Google Scholar 

  9. D. Ojeda-Guillén, R. D. Mota, and V. D. Granados, J. Math. Phys., 57, 062104 (2016).

  10. F. M. Toyama, Y. Nogami, and F. A. B. Coutinho, J. Phys. A: Math. Gen., 30, 2585 (1997).

    Article  ADS  Google Scholar 

  11. R. Szmytkowski and M. Gruchowski, J. Phys. A: Math. Gen., 34, 4991 (2001).

    Article  ADS  Google Scholar 

  12. N. Ferkous and A. Bounames, Phys. Lett A, 325, 21 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  13. R. de L. Rodrigues, Phys. Lett. A, 372, 2587 (2008).

  14. A. Bermudez, M. A. M. Delgedo, and A. Luis, Phys. Rev. A, 77, 063815 (2008).

  15. A. Bermudez, M. A. Martin-Delgado, and E. Solano, Phys. Rev. A, 76, 041801 (2007).

  16. E. Sadurni, J. M. Torres, and T. H. Seligman, J. Phys. A: Math. Theor., 43, 285204 (2010).

    Article  ADS  Google Scholar 

  17. A. Bermudez, M. A. Martin-Delgado, and E. Solano, Phys. Rev. A, 76, 041801 (2007).

  18. J. Benítez, R. P. M. Y. Romero, H. N. Núñez-Yépez, and A. L. Salas-Brito, Phys. Rev. Lett., 64, 1643 (1990); Erratum, Phys. Rev. Lett., 65, 2085 (1990).

  19. B. P. Mandal and S. Verma, Phys. Lett. A, 374, 1021 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  20. A. Bermudez, M. A. Martin-Delgado, and E. Solano, Phys. Rev. A, 76, 041801 (2007).

  21. J. M. Torres, E. Sadurmi, and T. H. Seligman, AIP Conf. Proc., 1323, 301 (2010).

    Article  ADS  Google Scholar 

  22. A. S.-F. Obada, M. M. A. Ahmed, M. Abu-Shady, and H. F. Habeba, J. Russ. Laser Res., 40, 132 (2019).

    Article  Google Scholar 

  23. W. Greiner, Relativistic Quantum Mechanics: Wave Equations, Springer, Berlin (2000).

    Book  Google Scholar 

  24. M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge University Press (1997).

  25. E. Sadurni, J. M. Torres, and T. H. Seligman, J. Phys. A: Math. Theor., 43, 285204 (2010).

    Article  ADS  Google Scholar 

  26. M. S. Abdalla, M. M. A. Ahmed, and A.-S. F. Obada, Laser Phys., 25, 065204 (2015).

    Article  ADS  Google Scholar 

  27. J. von Neumann, Mathematical Fundations of Quantum Mechanics, Princaton University Press (1955).

  28. F. Minter, M. Ku\( \tilde{\mathrm{s}} \), and A. Buchleitner, Phys. Rev. Lett., 95, 160 (2005).

    Google Scholar 

  29. M. Abdel-Aty, Prog. Quantum Electron., 31, 1 (2007).

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, Al-Azher University, Nassr City, 11884, Egypt

    A. S.-F. Obada & M. M. A. Ahmed

  2. Department of Mathematics and Computer Science Faculty of Science, Menoufia University, Shebin Elkom, 32511, Egypt

    M. Abu-Shady & H. F. Habeba

Authors
  1. A. S.-F. Obada
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  2. M. M. A. Ahmed
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  3. M. Abu-Shady
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  4. H. F. Habeba
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Correspondence to H. F. Habeba.

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Obada, A.SF., Ahmed, M.M.A., Abu-Shady, M. et al. Effect of an External Magnetic Field on Some Statistical Properties of the 2+1 Dirac–Moshinsky Oscillator. J Russ Laser Res 40, 328–339 (2019). https://doi.org/10.1007/s10946-019-09808-1

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  • DOI: https://doi.org/10.1007/s10946-019-09808-1

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