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Geometric phase and entanglement for a single qubit interacting with deformed-states superposition

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An Erratum to this article was published on 13 March 2013

Abstract

The geometric phase and quantum entanglement for a nonlinear field-atom system are described quantitatively in terms of different parameters. Specifically, considering a deformed Schrödinger cat interacting with a qubit and taking into account the time dependent of the system coupling. The results show that the initial state setting, atomic motion, photon number and deformation play important roles in the evolution of the system dynamics, nonlocal correlation and geometric phase. An interesting correlation between the entanglement and geometric phase is observed during the time evolution. The presented system is very useful to generate and maintain high amount of entanglement through controlling the phase variation of the system under consideration. We test this observation with experimentally accessible parameters and some new aspects are obtained.

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References

  1. Pancharatnam, S.: Proc. Indian Acad. Sci. A 44, 247 (1956)

    MathSciNet  Google Scholar 

  2. Berry, M.V.: Proc. R. Soc. Lond. Ser. A 392, 45 (1984)

    Article  ADS  MATH  Google Scholar 

  3. Jordan, T.F.: Phys. Rev. A 38, 1590 (1988)

    Article  ADS  Google Scholar 

  4. Samuel, J., Bhandari, R.: Phys. Rev. Lett. 60, 2339 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  5. Berry, M.V.: J. Mod. Opt. 34, 1401 (1987)

    Article  ADS  MATH  Google Scholar 

  6. Weinfurter, H., Banudrek, G.: Phys. Rev. Lett. 64, 1318 (1990)

    Article  ADS  Google Scholar 

  7. Wu, Y.-S., Li, H.-Z.: Phys. Rev. B 38, 11907 (1988)

    Article  ADS  Google Scholar 

  8. Tarasov, V.E.: J. Phys. A 35, 5207 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Sjoqvist, E., Pati, A.K., Ekert, A.K., Anandan, J.S., Ericsson Ericsson, M., Oi, D.K.L., Vedral, V.: Phys. Rev. Lett. 85, 2845 (2000)

    Article  ADS  Google Scholar 

  11. Vedral, V.: J. Mod. Opt. 47, 2501 (2000)

    MathSciNet  ADS  MATH  Google Scholar 

  12. Abdel-Aty, M.: J. Opt. B 5, 349 (2003)

    Article  ADS  Google Scholar 

  13. Abdel-Aty, M., Abdel-Khalek, S., Obada, A.-S.F.: Opt. Rev. 7, 499 (2000)

    Article  Google Scholar 

  14. Wagh, G., Rakhecha, V.C.: Phys. Lett. A 197, I12 (1995)

    Google Scholar 

  15. Lu, J.: Eur. Phys. J. D 5, 307 (1999)

    ADS  Google Scholar 

  16. Lawande, Q.V., Lawande, S.V., Joshi, A.: Phys. Lett. A. 251, 164 (1999)

    Article  ADS  Google Scholar 

  17. Abdel-Aty, M.: Phys. Lett. A 373, 3572 (2009)

    Article  ADS  MATH  Google Scholar 

  18. Bouchene, M.A., Abdel-Aty, M.: Phys. Rev. A 79, 055402 (2009)

    Article  ADS  Google Scholar 

  19. Pati, A.: Int. J. Quant. Inf. 1, 135 (2003)

    Article  MATH  Google Scholar 

  20. Drinfeld, V.G.: Quantum groups. In: Gleason, A.M. (ed.) Proceedings of the International Congress of Mathematics, Berkeley vol. I, p. 798. American Mathematicial Society, Providence (1986)

  21. Biedenharn, L.C.: J. Phys. A 22, L873 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Macfarlane, A.J.: J. Phys. A 22, 4581 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. Man’ko, V.I., Marmo, G., Solimeno, S., Zaccaria, F.: Int. J. Mod. Phys. A. 8, 3577 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Man’ko, V.I., Marmo, G., Zaccaria, F., Sudarshan, E.C.G.: Phys. Scr. 55, 528 (1997)

    Article  ADS  Google Scholar 

  25. Bonatsos, D., Daskaloyannis, C., Kokkotas, K.: J. Phys. A Math. Gen. 24, L795 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Ballesteros, A., Civitarese, O., Reboiro, M.: Phys. Rev. C 68, 044307 (2003)

    Article  ADS  Google Scholar 

  27. Dodonov, V.V.: J. Opt. B Quant. Semiclass. 4, R1 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  28. Katriel, J., Solomon, A.I.: Phys. Rev. A 49, 5149 (1994)

    Article  ADS  Google Scholar 

  29. Si-cong, J.S., Hong-yi, F.: Phys. Rev. A 49, 2277 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  30. Berrada, K., Benmoussa, A., Hassouni, Y.: Quant. Inf. Proc. 10, 575 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  31. Berrada, K., El Baz, M., Hassouni, Y.: J. Stat. Phys. 142, 510 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Berrada, K., El Baz, M., Hassouni, Y.: Rep. Math. Phys. 68, 23 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Berrada, K., Hassouni, Y.: Eur. Phys. J. D 61, 513 (2011)

    Article  ADS  Google Scholar 

  34. De Chiara, G., Palma, G.M.: Phys. Rev. Lett. 91, 090404 (2003)

    Article  Google Scholar 

  35. Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

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

    MATH  Google Scholar 

  37. Huver, S.D., Wildfeuer, C.F., Dowling, J.P.: Phys. Rev. A 78, 063828 (2008)

    Article  ADS  Google Scholar 

  38. Müstecaphoǧlu, Ö.E.: Phys. Rev. A 68, 023811 (2003)

    Article  Google Scholar 

  39. Sargent III, M., Scully, M.O., Lamb Jr, W.E.: Laser Physics. Addison-Wesley, Reading/Mass (1974)

    Google Scholar 

  40. Enaki, N.A., Ciobanu, N.: J. Mod. Opt. 55, 1557 (2008)

    Article  MATH  Google Scholar 

  41. Carmichael, H.J., Sanders, B.C.: Phys. Rev. A 60, 2497 (1999)

    Article  ADS  Google Scholar 

  42. Hood, C.J., Chapman, M.S., Lynn, T.W., Kimble, H.J.: Phys. Rev. Lett. 80, 4157 (1998)

    Article  ADS  Google Scholar 

  43. Berrada, K.: Opt. Commun. 285, 2227 (2012)

    Article  ADS  Google Scholar 

  44. Tsallis, C.: J. Stat. Phys. 52, 479 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. Braz, J.: Phys. 29, 1 (1999)

    Google Scholar 

  46. MacFarlane, A.J.: J. Phys. A 22, 4581 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. Berrada, K., El Baz, M., Hassouni, Y.: J. Stat. Phys. 142, 510 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. Aharonov, Y., Anandan, J.S.: Phys. Rev. Lett. 58, 1593 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  49. Sjöqvist, E., Pati, A.K., Ekert, A., Anandan, J.S., Ericsson, M., Oi, D.K.L., Vedral, V.: Phys. Rev. Lett. 85, 2845 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  51. Berrada, K., Fanchini, F.F., Abdel-Khalek, S.: Phys. Rev. A 85, 052315 (2012)

    Article  ADS  Google Scholar 

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Acknowledgments

K.B and S.A pleased to express his sincere gratitude for the hospitality at the ABDUS SALAM CENTRE FOR THEORETICAL PHYSICS where part of this work is done. C. H. Raymond Ooi is grateful for support by the Ministry of Higher Education (MOHE)/University of Malaya HIR Grant No. A-000004-50001.

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Authors and Affiliations

  1. The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Miramare-Trieste, Italy

    K. Berrada

  2. Laboratoire de Physique Théorique, Faculté des Sciences, Université Mohammed V-Agdal, Av. Ibn Battouta, B.P. 1014, Agdal Rabat, Morocco

    K. Berrada

  3. Department of Physics, Al-Imam Muhammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

    K. Berrada

  4. Mathematics Department, Faculty of Science, Sohag University, 82524 , Sohag, Egypt

    S. Abdel-Khalek

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

    S. Abdel-Khalek

  6. Department of Physics, University of Malaya, 50603, Kuala Lumpur, Malaysia

    C. H. Raymond Ooi

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  1. K. Berrada
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  2. S. Abdel-Khalek
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  3. C. H. Raymond Ooi
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Correspondence to K. Berrada.

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Berrada, K., Abdel-Khalek, S. & Raymond Ooi, C.H. Geometric phase and entanglement for a single qubit interacting with deformed-states superposition. Quantum Inf Process 12, 2177–2188 (2013). https://doi.org/10.1007/s11128-012-0510-8

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  • DOI: https://doi.org/10.1007/s11128-012-0510-8

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