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Relation between Berry phases and entanglement besides convergence of levels for two entangled spin-1/2 particles in magnetic fields

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Abstract

We study the effects of an extra static magnetic field, coupling with one of the two entangled spin-1/2 particles, on Berry phases and entanglement of the adiabatic eigensatates of the system, while the other spin interacts with a rotating magnetic field satisfying the adiabatic condition. This static magnetic field can be used for controlling the Berry phases and the entangled state of the system. The relation of the Berry phases and entanglement to Dzyaloshinski-Moriya interaction, coupling coefficient, and the magnetic fields are also investigated. The results demonstrate a close relationship between the Berry phases and pairwise entanglement (as measured by the so-called entanglement of formation). We show that reversing the sign of the static magnetic field can cause exchanges of the Berry phases and entanglement between the adiabatic states. It is illustrated that the geometric phases and entanglement are good indicators to detect the convergence of the levels and each convergence of levels corresponds to abrupt changes in the Berry phases and entanglement.

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References

  1. M.V. Berry, Proc. Roy. Soc. Lond. A 392, 45 (1984)

    Article  ADS  MATH  Google Scholar 

  2. Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  3. J. Samuel, B. Bhandari, Phys. Rev. Lett. 60, 2339 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  4. F. Wilczek, A. Zee, Phys. Rev. Lett. 52, 2111 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Uhlmann, Rep. Math. Phys. 24, 229 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. A. Uhlmann, Lett. Math. Phys. 21, 229 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. E. Sjöqvist, A.K. Pati, A. Ekert, A. Anandan, E. Ericsson, D.K.L. Oi, V. Vedral, Phys. Rev. Lett. 85, 2845 (2000)

    Article  ADS  Google Scholar 

  8. X.Y. Ge, M. Wadati, Phys. Rev. A 72, 052101 (2005)

    Article  ADS  Google Scholar 

  9. X.X. Yi, L.C. Wang, T.Y. Zheng, Phys. Rev. Lett. 92, 150406 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  10. H.Y. Sun, L.C. Wang, X.X. Yi, Phys. Lett. A 370, 119 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Y. Zhou, G.F. Zhang, Opt. Commun. 281, 5278 (2008)

    Article  ADS  Google Scholar 

  12. X. Li, Phys. Lett. A 372, 4980 (2008)

    Article  ADS  MATH  Google Scholar 

  13. S. Oh, Phys. Lett. A 373, 644 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. S.B. Zheng, G.C. Guo, Phys. Rev. Lett. 85, 2392 (2000)

    Article  ADS  Google Scholar 

  15. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Communication (Cambridge University Press, Cambridge, 2000)

  16. D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, Nature 390, 575 (1997)

    Article  ADS  Google Scholar 

  17. D. Deutsch, R. Jozsa, Proc. Roy. Soc. Lond. A 439, 553 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. B. Basu, Europhys. Lett. 73, 833 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  19. B. Basu, P. Bandyopadhyay, J. Phys. A: Math. Theor. 41, 055301 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  20. F.C. Lombardo, P.I. Villar, Phys. Rev. A 81, 022115 (2010)

    Article  ADS  Google Scholar 

  21. C.S. Castro, M.S. Sarandy, Phys. Rev. A 83, 042334 (2011)

    Article  ADS  Google Scholar 

  22. S.N. Sandhya, S. Banerjee, arXiv:1103.2587v2 [quant-ph]

  23. D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998)

    Article  ADS  Google Scholar 

  24. D.P. DiVincenzo et al., Nature 408, 339 (2000)

    Article  ADS  Google Scholar 

  25. I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958)

    Article  ADS  Google Scholar 

  26. T. Moriya, Phys. Rev. Lett. 4, 228 (1960)

    Article  ADS  Google Scholar 

  27. J.Z. Zhao, X.Q. Wang, T. Xiang, Z.B. Su, L. Yu, Phys. Rev. Lett. 90, 207204 (2003)

    Article  ADS  Google Scholar 

  28. I. Tsukada, J. Takeya, T. Masuda, K. Uchinokura, Phys. Rev. Lett. 87, 127203 (2001)

    Article  ADS  Google Scholar 

  29. M.K. Kwan, Z.N. Gurkan, L.C. Kwek, Phys. Rev. A 77, 062311 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  30. C.H. Bennett, D.P. DiVincenzo, J. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  31. F. Mintert, A.R.R. Carvalho, M. Kuś, A. Buchleitner, Phys. Rep. 415, 207 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  32. W.K. Wootters, Quantum Inf. Comput. 1, 27 (2001)

    MathSciNet  MATH  Google Scholar 

  33. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  34. J.R. Walkup, M. Dunn, D.K. Watson, T.C. Germann, Phys. Rev. A 58, 4668 (1998)

    Article  ADS  Google Scholar 

  35. G. Moruzzi, The Hanle Effect and Level-Crossing Spectroscopy (Kluwer Academic Publishers, Norwell, 1991)

  36. B.H. Bransden, Charge Exchange and the Theory of Ion-Atom Collisions (Oxford University Press, Oxford, 1992)

  37. W.E. Lamb, Phys. Rev. 105, 559 (1957)

    Article  ADS  Google Scholar 

  38. T. Bergeman, Phys. Rev. Lett. 52, 1685 (1984)

    Article  ADS  Google Scholar 

  39. L. Marcassa, S. Muniz, E. de Queiroz, S. Zilio, V. Bagnato, J. Weiner, P.S. Julienne, K.-A. Suominen, Phys. Rev. Lett. 73, 1911 (1994)

    Article  ADS  Google Scholar 

  40. F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 2006)

  41. R.G. Unanyan, N.V. Vitanov, K. Bergmann, Phys. Rev. Lett. 87, 137902 (2001)

    Google Scholar 

  42. L.D. Landau, E.M. Lifshitz, Quantum Mechanics, 2nd edn. (Pergamon Press, Oxford, 1965)

  43. C. Zener, Proc. Roy. Soc. Lond. A 137, 696 (1932)

    Article  ADS  Google Scholar 

  44. M. Bhattacharya, C. Raman, Phys. Rev. A 75, 033405 (2007)

    Article  ADS  Google Scholar 

  45. S. Oh, Z. Huang, U. Peskin, S. Kais, Phys. Rev. A 78, 062106 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  46. Shi-Liang Zhu, Phys. Rev. Lett. 96, 077206 (2006)

    Article  ADS  Google Scholar 

  47. Shi-Liang Zhu, Int. J. Mod. Phys. B 22, 561 (2008)

    Article  ADS  MATH  Google Scholar 

  48. Y.Q. Ma, S. Chen, Phys. Rev. A 79, 022116 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  49. A.I. Nesterov, S.G. Ovchinnikov, Phys. Rev. E 78, 015202(R) (2008)

    Article  ADS  Google Scholar 

  50. K.M. O’Connors, W.K. Wootters, Phys. Rev. A 63, 052302 (2001)

    Article  ADS  Google Scholar 

  51. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. J. Karthik, A. Sharma, A. Lakshminarayan, Phys. Rev. A 75, 022304 (2007)

    Article  ADS  Google Scholar 

  53. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2001)

  54. A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002)

    Article  ADS  Google Scholar 

  55. S.J. Gu, H.Q. Lin, Y.Q. Li, Phys. Rev. A 68, 042330 (2003)

    Article  ADS  Google Scholar 

  56. S.J. Gu, G.S. Tian, H.Q. Lin, Phys. Rev. A 71, 052322 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  57. J.A. Jones et al., Nature 403, 869 (2000)

    Article  ADS  Google Scholar 

  58. C. Macchiavello, G.M. Palma, A. Zeilinger, Quantum Computation and Quantum Information Theory (World Scientific, Singapore, 2000)

  59. A. Ekert et al., J. Mod. Opt. 47, 2501(2000)

  60. Y. Shi, Ann. Phys. 325, 1207 (2010)

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Physics Department, Faculty of Sciences, Urmia University, P.B. 165, Urmia, Iran

    M. Amniat-Talab & H. Rangani Jahromi

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  1. M. Amniat-Talab
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  2. H. Rangani Jahromi
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Correspondence to H. Rangani Jahromi.

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Amniat-Talab, M., Rangani Jahromi, H. Relation between Berry phases and entanglement besides convergence of levels for two entangled spin-1/2 particles in magnetic fields. Eur. Phys. J. D 66, 211 (2012). https://doi.org/10.1140/epjd/e2012-30085-5

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