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Berry’s phase for displaced Landau-He-McKellar-Wilkens states

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Abstract.

Displaced states for neutral particles which possess a permanent electric dipole moment are built in the presence of a magnetic field. Then, by performing an adiabatic cyclic evolution, it is shown that Abelian and non-Abelian Berry phases can be obtained for the displaced states based on the Landau-He-McKellar-Wilkens quantization (L.R. Ribeiro et al., Phys. Lett. A 348, 135 (2006)).

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References

  1. R.J. Glauber, Phys. Rev. 131, 2766 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  2. M. Venkata Satyanarayana, Phys. Rev. D 32, 400 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  3. P. Král, J. Mod. Opt. 37, 889 (1990)

    Article  ADS  Google Scholar 

  4. F.A.M. de Oliveira, M.S. Kim, P.L. Knight, V. Buzek, Phys. Rev. A 41, 2645 (1990)

    Article  ADS  Google Scholar 

  5. H. Moya-Cessa, J. Mod. Opt. 42, 1741 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  6. A.-S.F. Obada, G.M. Abd Al-Kader, J. Mod. Opt. 46, 263 (1999)

    Article  ADS  Google Scholar 

  7. R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D.N. Christodoulides, A. Szameit, Phys. Rev. Lett. 107, 103601 (2011)

    Article  ADS  Google Scholar 

  8. A.I. Lvovsky, S.A. Babichev, Phys. Rev. A 66, 011801(R) (2002)

    Article  ADS  Google Scholar 

  9. D.T. Smithey et al., Phys. Rev. Lett. 70, 1244 (1993)

    Article  ADS  Google Scholar 

  10. K. Banaszek, K. Wodkiewicz, Phys. Rev. A 58, 4345 (1998)

    Article  ADS  Google Scholar 

  11. A. Kuzmich, I.A. Walmsley, L. Mandel, Phys. Rev. Lett. 85, 1349 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  12. A. Kuzmich, I.A. Walmsley, L. Mandel, Phys. Rev. A 64, 063804 (2001)

    Article  ADS  Google Scholar 

  13. Da-Bao Yang, Jing-Ling Chen, Commun. Theor. Phys. 56, 247 (2011)

    Article  ADS  Google Scholar 

  14. Da-Bao Yang, Ying Chen, Fu-Lin Zhang, Jing-Ling Chen, J. Phys. B: At. Mol. Opt. Phys. 44, 075502 (2011)

    Article  ADS  Google Scholar 

  15. L.D. Landau, Z. Phys. 64, 629 (1930)

    Article  ADS  Google Scholar 

  16. L.D. Landau, E.M. Lifshitz, Quantum Mechanics, the nonrelativistic theory, 3rd edition (Pergamon, Oxford, 1977)

  17. W.-L. Yang, J.-L. Chen, Phys. Rev. A 75, 024101 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  18. R.E. Prange, S.M. Girvin (Editors), The Quantum Hall Effect (Springer-Verlag, New York, 1990)

  19. B. Paredes, P. Fedichev, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 87, 010402 (2001)

    Article  ADS  Google Scholar 

  20. B. Paredes, P. Zoller, J.I. Cirac, Solid State Commun. 127, 155 (2003)

    Article  ADS  Google Scholar 

  21. A. Comtet, Ann. Phys. (N.Y.) 173, 185 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  22. C. Grosche, Ann. Phys. (N.Y.) 187, 110 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  23. G.V. Dunne, Ann. Phys. (N.Y.) 215, 233 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  24. Y. Aharanov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Ericsson, E. Sjöqvist, Phys. Rev. A 65, 013607 (2001)

    Article  ADS  Google Scholar 

  26. L.R. Ribeiro, C. Furtado, J.R. Nascimento, Phys. Lett. A 348, 135 (2006)

    Article  ADS  Google Scholar 

  27. X.-G. He, B.H.J. McKellar, Phys. Rev. A 47, 3424 (1993)

    Article  ADS  Google Scholar 

  28. M. Wilkens, Phys. Rev. Lett. 72, 5 (1994)

    Article  ADS  Google Scholar 

  29. C. Furtado, J.R. Nascimento, L.R. Ribeiro, Phys. Lett. A 358, 336 (2006)

    Article  ADS  Google Scholar 

  30. K. Bakke, C. Furtado, Phys. Rev. A 80, 032106 (2009)

    Article  ADS  Google Scholar 

  31. K. Bakke, Phys. Rev. A 81, 052117 (2010)

    Article  ADS  Google Scholar 

  32. M.V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  35. A. Tomita, R.Y. Chiao, Phys Rev. Lett. 57, 937 (1986)

    Article  ADS  Google Scholar 

  36. R. Simon, H.J. Kimble, E.C.G. Sudarshan, Phys Rev. Lett. 61, 19 (1988)

    Article  ADS  Google Scholar 

  37. T. Bitter, D. Dubbers, Phys. Rev. Lett. 59, 251 (1987)

    Article  ADS  Google Scholar 

  38. R. Tycko, Phys. Rev. Lett. 58, 2281 (1987)

    Article  ADS  Google Scholar 

  39. J.Q. Shen, Eur. Phys. J. D 30, 259 (2004)

    Article  ADS  Google Scholar 

  40. J.Q. Shen, J. Opt. B 6, L13 (2004)

    Article  ADS  Google Scholar 

  41. K. Bakke, C. Furtado, Phys. Rev. A 87, 012130 (2013)

    Article  ADS  Google Scholar 

  42. J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1975)

  43. J.P. Dowling, C. Williams, J.D. Franson, Phys. Rev. Lett. 83, 2486 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  44. C. Furtado, G. Duarte, Phys. Scr. 71, 7 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  45. M.W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, D.S. Hall, Nature 505, 657 (2014)

    Article  ADS  Google Scholar 

  46. J. Anandan, Phys. Lett. A 138, 347 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  47. J. Anandan, Phys. Rev. Lett. 85, 1354 (2000)

    Article  ADS  Google Scholar 

  48. A.Ya. Silenko, Russ. Phys. J. 48, 788 (2005)

    Article  Google Scholar 

  49. W. Greiner, Relativistic Quantum Mechanics: Wave Equations, 3rd edition (Springer, Berlin, 2000)

  50. K. Bakke, J.R. Nascimento, C. Furtado, Phys. Rev. D 78, 064012 (2008)

    Article  ADS  Google Scholar 

  51. A. Feldman, A.H. Kahn, Phys. Rev. B 1, 4584 (1970)

    Article  ADS  Google Scholar 

  52. M.H. Johnson, B.A. Lippmann, Phys. Rev. 76, 828 (1949)

    Article  ADS  MathSciNet  Google Scholar 

  53. A. Wünsche, Quantum Opt. 3, 359 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  54. A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger, The geometric phase in quantum systems: foundations, mathematical concepts and applications in molecular and condensed matter physics (Springer-Verlag, New York, 2003)

  55. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  56. P. Zanardi, M. Rasetti, Phys. Lett. A 264, 94 (1999)

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Lemos de Melo, J., Bakke, K. & Furtado, C. Berry’s phase for displaced Landau-He-McKellar-Wilkens states. Eur. Phys. J. Plus 131, 165 (2016). https://doi.org/10.1140/epjp/i2016-16165-8

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  • DOI: https://doi.org/10.1140/epjp/i2016-16165-8

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