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Quantum holonomies for displaced Landau–Aharonov–Casher states

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Abstract

We construct displaced Fock states for a Landau–Aharonov–Casher system for neutral particles. Abelian and non-Abelian geometric phases can be obtained in an adiabatic cyclic evolution using this displaced states. Moreover, we show that a possible logical base related to the angular momenta of the neutral particle with permanent magnetic dipole moment can be defined, and then quantum holonomies for specific paths can be built and used to implement one-qubit quantum gates.

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References

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Aharonov, Y., Casher, A.: Phys. Rev. Lett. 53, 319 (1984)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Wünsche, A.: Quantum Opt. 3, 359 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  20. Keil, R., et al.: Phys. Rev. Lett. 107, 103601 (2011)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  22. Ekert, A., Ericsson, M., Hayden, P., Inamory, H., Jones, J.A., Oi, D.K.L., Vedral, V.: J. Mod. Opt. 47, 2501 (2000)

    Article  ADS  MATH  Google Scholar 

  23. Vedral, V.: Int. J. Quantum Inf. 1, 1 (2003)

    Article  MATH  Google Scholar 

  24. Kuvshinov, V.I., Kuzmin, A.V.: Phys. Lett. A 316, 391 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Margolin, A.E., Strazhev, V.I., Tregubovich, A.Y.: Phys. Lett. A 303, 131 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Bakke, K., Furtado, C.: Quantum Inf. Comput. 11, 0444 (2011)

    MathSciNet  Google Scholar 

  27. Bakke, K., Furtado, C.: Phys. Lett. A 375, 3956 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  29. Bohm, A., Mostafazadeh, A., Koizumi, H., Niu, Q., Zwanziger, J.: The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts and Applications in Molecular and Condensed Matter Physics. Springer, New York (2003)

    Book  Google Scholar 

  30. Mead, C.A., Truhlar, D.G.: J. Chem. Phys. 77, 6090 (1982)

    Article  ADS  Google Scholar 

  31. Mead, C.A.: J. Chem. Phys. 78, 807 (1983)

    Article  ADS  Google Scholar 

  32. Mead, C.A.: Rev. Mod. Phys. 64, 51 (1992)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  34. Mead, C.A., Truhlar, D.G.: J. Chem. Phys. 70, 2284 (1979)

    Article  ADS  Google Scholar 

  35. Mead, C.A.: Chem. Phys. 49, 23 (1980)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    MATH  Google Scholar 

  38. Lloyd, S.: Phys. Rev. Lett. 75, 346 (1995)

    Article  ADS  Google Scholar 

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

    Google Scholar 

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Acknowledgments

We would like to thank CNPq, CAPES/NANOBIOTEC, CNPQ/PNPD, CNPQ/ Universal for financial support.

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Authors and Affiliations

  1. Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970 , João Pessoa, PB, Brazil

    J. Lemos de Melo, K. Bakke & C. Furtado

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  1. J. Lemos de Melo
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  2. K. Bakke
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  3. C. Furtado
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Correspondence to C. Furtado.

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de Melo, J.L., Bakke, K. & Furtado, C. Quantum holonomies for displaced Landau–Aharonov–Casher states. Quantum Inf Process 13, 1563–1572 (2014). https://doi.org/10.1007/s11128-014-0751-9

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  • DOI: https://doi.org/10.1007/s11128-014-0751-9

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