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Entropic uncertainty for two atoms interacting with a cavity field under the influence of two photons (off-resonance case)

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Journal of Russian Laser Research Aims and scope

Abstract

In this paper, we introduce a Hamiltonian model describing the interaction of two photons with two two-level atoms and a degenerate parametric amplifier. In the near-resonance case, we obtain an analytic solution of the evolution equation for the wave function in the Schr¨odinger picture and use the obtained result for discussing the atomic inversion, the purity, and the phenomenon of squeezing. We show that the phenomenon of superstructure appears in the atomic inversion in the presence of detuning (with parameter Δ) and coupling (with parameter λ3). Our study of the purity shows that the system is always in a mixed state, and the maximum value of entanglement occurs around ~0.6. Also we show that detuning leads to a reduction in the value of squeezing for all quadrature variances. In contrast, the coupling parameter leads to an increase in the value of squeezing. However, for the usual single-mode squeezing (of quadratures) the effect of detuning consists in increase in the squeezing period.

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References

  1. A. Wallraff, D. I. Schuster, A. Blais, et al., Nature, 431, 162 (2004).

    Article  ADS  Google Scholar 

  2. I. Chiorescu, P. Bertet, K. Semba, et al., Nature, 431, 159 (2004).

    Article  ADS  Google Scholar 

  3. J. Johansson, S. Saito, T. Meno, et al., Phys. Rev. Lett., 96, 127006 (2006).

    Article  ADS  Google Scholar 

  4. A. A. Houck, D. I. Schuster, J. M. Gambetta, et al., Nature, 449, 328 (2007).

    Article  ADS  Google Scholar 

  5. O. Astafiev, K. Inomata, A. O. Niskanen, et al., Nature, 449, 588 (2007).

    Article  ADS  Google Scholar 

  6. M. A. Sillanpāă, J. I. Park, and R. W. Simmonds, Nature, 449, 438 (2007).

    Article  ADS  Google Scholar 

  7. J. Majer, J. M. Chow, J. M. Gambetta, et al., Nature, 449, 443 (2007).

    Article  ADS  Google Scholar 

  8. A. Wallraff, D. I. Schuster, A. Blais, et al., Phys. Rev. Lett., 99, 050501 (2007).

    Article  ADS  Google Scholar 

  9. R. J. Thompson, G. Rempe and H. J. Kimble, Phys. Rev. Lett., 68, 1132 (1992).

    Article  ADS  Google Scholar 

  10. H. Mabuchi and A. C. Doherty, Science, 298, 1372 (2002).

    Article  ADS  Google Scholar 

  11. S. Haroche and J. M. Raimond, Exploring the Quantum, Oxford University Press, New York (2006).

    Book  MATH  Google Scholar 

  12. F. Deppe, M. Matteo, A. Mariantoni, et al., Nature, 450, 686 (2008).

    Google Scholar 

  13. 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 

  14. E. M. Khalil, M. S. Abdalla, and A. S.-F. Obada, J. Phys. B, 43, 095507 (2010).

    Article  ADS  Google Scholar 

  15. M. Abdel-Aty, M. S. Abdalla, and A. S.-F.Obada, J. Phys. B: At. Mol. Opt. Phys., 37, 775 (2004).

    Article  ADS  Google Scholar 

  16. A. S.-F. Obada, M. Abdel-Aty, and M. S. Abdalla, Laser Phys. Lett., 2, 208 (2005).

    Article  ADS  Google Scholar 

  17. B. W. Shore and P. L. Knight, J. Mod. Opt., 40, 1195 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. A. K. Ekert, Phys. Rev. Lett., 67, 661 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, Phys. Rev. Lett., 69, 1293 (1992).

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  22. S. F. Huelga, C. Macchiavello, T. Pellizzari, et al., Phys. Rev. Lett., 79, 3865 (1997).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. M. Murao, M. B. Plenio, S. Popescue, et al., Phys. Rev. A, 57, R4075 (1998).

    Article  ADS  Google Scholar 

  25. A. Carlson, M. Koashi, and N. Imoto, Phys. Rev. A, 59, 162 (1999).

    Article  ADS  Google Scholar 

  26. P. W. Shor, Phys. Rev. A, 52, R2493 (1995).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. S. J. D. Phoenix and P. L. Knight, Ann. Phys. (N.Y), 186, 381 (1998).

    Article  ADS  Google Scholar 

  30. V. Buźek, H. Moya-Cessa, and P. L. Knight, Phys. Rev. A, 45, 8190 (1992).

    Article  ADS  Google Scholar 

  31. V. I. Man’ko, G. Marmo, A. Porzio, et al., Phys. Scr., 83, 045001 (2011).

    Article  ADS  Google Scholar 

  32. P. L. Knight and P. M. Radamore, Phys. Lett. A, 90, 342 (1982).

    Article  ADS  Google Scholar 

  33. M. S. Abdalla, E. Lashin, and G. Sadiek, J. Phys. B, 41, 015502 (2008).

    Article  ADS  Google Scholar 

  34. G. Sadiek, E. Lashin, and M. S. Abdalla, Physica B, 404, 1719 (2009).

    Article  ADS  Google Scholar 

  35. M. S. Abdalla and M. M. A. Ahmed, Opt. Commun., 284, 1933 (2011).

    Article  ADS  Google Scholar 

  36. M. A. Man’ko and V. I. Man’ko, Found Phys., 41, 330 (2011).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).

    Article  ADS  Google Scholar 

  38. V. I. Man’ko, G. Marmo, A. Simoni, and F. Ventriglia, Adv. Sci. Lett., 2, 517 (2009).

    Article  Google Scholar 

  39. S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, Eur. Phys. J. B, 52, 191 (2006).

    Article  ADS  Google Scholar 

  40. J. Sanchez-Ruiz, Phys. Lett. A, 201, 125 (1995).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. J. Sanchez-Ruiz, Phys. Lett. A, 244, 189 (1998).

    Article  ADS  Google Scholar 

  42. J. Sanchez-Ruiz, Phys. Lett. A, 173, 233 (2003).

    Article  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  45. H. I. Yoo and J. H. Eberly, Phys. Rep., 118, 239 (1981).

    Article  ADS  Google Scholar 

  46. M. S. Abdalla, Physica A, 210, 461 (1994).

    Article  ADS  Google Scholar 

  47. M. S. Abdalla, Physica A, 202, 301 (1994).

    Article  ADS  Google Scholar 

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Authors and Affiliations

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

    E. M. Khalil

  2. Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    M. Sebawe Abdalla

Authors
  1. E. M. Khalil
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  2. M. Sebawe Abdalla
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Correspondence to M. Sebawe Abdalla.

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Khalil, E.M., Abdalla, M.S. Entropic uncertainty for two atoms interacting with a cavity field under the influence of two photons (off-resonance case). J Russ Laser Res 33, 128–142 (2012). https://doi.org/10.1007/s10946-012-9267-x

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  • DOI: https://doi.org/10.1007/s10946-012-9267-x

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