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Geometric phase for mixed states

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Laser Physics

Abstract

We present a kinematic approach for obtaining the geometric phase of a mixed state under nonunitary evolution. This phase is gauge-invariant and measurable and leads to well-known results for unitary evolution.

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References

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

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  3. J. Anandan and Y. Aharonov, Phys. Rev. D 38, 1863 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  4. S. Pancharatnam, Proc.-Indian Acad. Sci., Sect. A 44, 247 (1956).

    MathSciNet  Google Scholar 

  5. J. Samuel and R. Bhandari, Phys. Rev. Lett. 60, 2339 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  6. N. Mukunda and R. Simon, Ann. Phys. (N. Y.) 228, 205 (1993).

    ADS  MathSciNet  Google Scholar 

  7. A. K. Pati, Phys. Rev. A 52, 2576 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  8. A. K. Pati, J. Phys. A 28, 2087 (1995).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. J. A. Jones, V. Vedral, A. Ekert and G. Castagnoli, Nature 403, 869 (1999).

    ADS  Google Scholar 

  10. A. K. Ekert, M. Ericsson, P. Hayden, et al., J. Mod. Opt. 47, 2501 (2000).

    ADS  MathSciNet  Google Scholar 

  11. A. Uhlmann, Rep. Math. Phys. 24, 229 (1986); Lett. Math. Phys. 21, 229 (1991).

    MATH  MathSciNet  Google Scholar 

  12. E. Sjöqvist, A. K. Pati, A. Ekert, et al., Phys. Rev. Lett. 85, 2845 (2000).

    Article  ADS  Google Scholar 

  13. K. Singh, D. M. Tong, K. Basu, et al., Phys. Rev. A 67, 032 106 (2003).

  14. E. Sjöqvist, Phys. Rev. A 62, 022 109 (2000).

    Google Scholar 

  15. B. Hessmo and E. Sjöqvist, Phys. Rev. A 62, 062301 (2000).

    Google Scholar 

  16. D. M. Tong, L. C. Kwek, and C. H. Oh, J. Phys. A 36, 1149 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  17. D. M. Tong, E. Sjoqvist, L. C. Kwek, et al., Phys. Rev. A 68, 022106 (2003).

  18. M. Ericsson, A. K. Pati, E. Sjöqvist, et al., Phys. Rev. Lett. 91, 090 405 (2003).

  19. N. Manini and F. Pistolesi, Phys. Rev. Lett. 85, 3067 (2000).

    Article  ADS  Google Scholar 

  20. S. Filipp and E. Sjöqvist, Phys. Rev. Lett. 90, 050403 (2003).

    Google Scholar 

  21. S. Filipp and E. Sjöqvist, Phys. Rev. A 68, 042112 (2003).

    Google Scholar 

  22. J. F. Du, P. Zou, M. Shi, L. C. Kwek, et al., Phys. Rev. Lett. 91, 100403 (2003).

  23. Gabriele De Chiara and G. Massimo Palma, Phys. Rev. Lett. 91, 090404 (2003).

  24. M. Ericsson, E. Sjöqvist, J. Brannlund, et al., Phys. Rev. A 67, 020101 (2003).

  25. A. Carollo, I. Fuentes-Guridi, M. Franca Santos and V. Vedral, Phys. Rev. Lett. 90, 160402 (2003).

    Google Scholar 

  26. J. G. Peixoto de Faria, A. F. R. de Toledo Piza, and M. C. Nemes, Europhys. Lett. 62, 782 (2003).

    Article  ADS  Google Scholar 

  27. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. A. Carollo, I. Fuentes-Guridi, M. Franca Santos, and V. Vedral, Phys. Rev. Lett. 90, 160402 (2003).

    Google Scholar 

  29. D. M. Tong, E. Sjöqvist, L. C. Kwek, and C. H. Oh, Phys. Rev. Lett. 93, 080405 (2004).

    Google Scholar 

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Original Text © Astro, Ltd., 2006.

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Kwek, L.C., Tong, D.M., Chen, J.L. et al. Geometric phase for mixed states. Laser Phys. 16, 398–401 (2006). https://doi.org/10.1134/S1054660X06020344

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  • DOI: https://doi.org/10.1134/S1054660X06020344

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