The European Physical Journal B

, Volume 83, Issue 4, pp 457–463 | Cite as

Entanglement of electronic subbands and coherent superposition of spin states in a Rashba nanoloop

  • R. Safaiee
  • M. M. Golshan
Regular Article Mesoscopic and Nanoscale Systems


The present work is concerned with an analysis of the entanglement between the electronic coherent superpositions of spin states and subbands in a quasi-one-dimensional Rashba nanoloop acted upon by a strong perpendicular magnetic field. We explicitly include the confining potential and the Rashba spin-orbit coupling into the Hamiltonian and then proceed to calculate the von Neumann entropy, a measure of entanglement, as a function of time. An analysis of the von Neumann entropy demonstrates that, as expected, the dynamics of entanglement strongly depends upon the initial state and electronic subband excitations. When the initial state is a pure one formed by a subband excitation and the z-component of spin states, the entanglement exhibits periodic oscillations with local minima (dips). On the other hand, when the initial state is formed by the subband states and a coherent superposition of spin states, the entanglement still periodically oscillates, exhibiting stronger correlations, along with elimination of the dips. Moreover, in the long run, the entanglement for the latter case undergoes the phenomenon of collapse-revivals. This behaviour is absent for the first case of the initial states. We also show that the degree of entanglement strongly depends upon the electronic subband excitations in both cases.


Spin State Density Operator Time Evolution Operator Coherent Superposition Electronic Spin State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    M.A. Eriksson, M. Friesen, S.N. Coppersmith, R. Joynt, L.J. Klein, K. Slinker, C. Tahan, B.N. Mooney, J.O. Chu, S.J. Koester, Quantum Inf. Process. 3, 133 (2004)MATHCrossRefGoogle Scholar
  2. 2.
    D. Loss, G. Burkard, D.P. DiVincenzo, J. Nanopart. Res. 2, 401 (2000)CrossRefGoogle Scholar
  3. 3.
    R. Hanson, L.H. Willems vanBeveren, I.T. Vink, J.M. Elzerman, W.J.M. Naber, F.H.L. Koppens, L.P. Kouwenhoven, L.M.K. Vandersypen, Phys. Rev. Lett. 94, 196802 (2005) ADSCrossRefGoogle Scholar
  4. 4.
    D. Stepanenko, N.E. Bonesteel, Phys. Rev. Lett. 93, 140501 (2004) ADSCrossRefGoogle Scholar
  5. 5.
    T.C. Wei, K. Nemoto, P.M. Goldbart, P.G. Kwiat, W.J. Munro, F. Verstraete, Phys. Rev. A 67, 022110 (2003) and refrences thereinADSCrossRefGoogle Scholar
  6. 6.
    C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993) MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Y. Zhou, G.-F. Zhang, Eur. Phys. J. D 47, 227 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    G. Burkard, D. Loss, D.P. DiVincenzo, Phys. Rev. B 59, 2070 (1999) ADSCrossRefGoogle Scholar
  10. 10.
    G. Burkard, H.-A. Engel, D. Loss, Fortschr. Phys. 48, 965 (2000)CrossRefGoogle Scholar
  11. 11.
    J. Schliemann, D. Loss, A.H. MacDonald, Phys. Rev. B 63, 085311 (2001) ADSCrossRefGoogle Scholar
  12. 12.
    A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, K. Peng, Phys. Rev. A 78, 013828 (2008) ADSCrossRefGoogle Scholar
  13. 13.
    P.C. Haljan, K.-A. Brickman, L. Deslauriers, P.J. Lee, C. Monroe, Phys. Rev. Lett. 94, 153602 (2005) ADSCrossRefGoogle Scholar
  14. 14.
    M.S. Sherwin, A. Imamoglu, T. Montroy, Phys. Rev. A 60, 3508 (1999) ADSCrossRefGoogle Scholar
  15. 15.
    T.B. Pittman, J.D. Franson, Phys. Rev. A 66, 062302 (2002) ADSCrossRefGoogle Scholar
  16. 16.
    V. Corato, C. Granata, S. Rombetto, B. Ruggiero, M. Russo, R. Russo, P. Silvestrini, A. Vettoliere, IEEE Trans. Appl. Supercond. 17, 132 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    T. Koga, J. Nitta, M. van Veenhuizen, Phys. Rev. B 70, R161302 (2004) ADSCrossRefGoogle Scholar
  18. 18.
    Y.A. Bychkov, E.I. Rashba, J. Phys. C 17, 6039 (1984) ADSCrossRefGoogle Scholar
  19. 19.
    P. Stano, Ph. D. thesis, University of Regensburg, 2007Google Scholar
  20. 20.
    M. Trushin, Ph. D. thesis, University of Hamburg, 2005Google Scholar
  21. 21.
    M.J. Yang, C.H. Yang, Y.B. Lyanda-Geller, Physica E 22, 304 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    M.J. Yang, C.H. Yang, Y.B. Lyanda-Geller, Europhys. Lett. 66, 826 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    M.P. Trushin, A.L. Chudnovskiy, Eur. Phys. J. B 52, 547 (2006)ADSMATHCrossRefGoogle Scholar
  24. 24.
    M.P. Trushin, A.L. Chudnovskiy, Physica E 34, 397 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    S. Debald, C. Emary, Phys. Rev. Lett. 94, 226803 (2005) ADSCrossRefGoogle Scholar
  26. 26.
    B.K. Nikolić, S. Souma, Phys. Rev. B 71, 195328 (2005) ADSCrossRefGoogle Scholar
  27. 27.
    R. Safaiee, M.M. Golshan, N. Foroozani, J. Stat. Mech. P11014, (2009)Google Scholar
  28. 28.
    E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935)ADSCrossRefGoogle Scholar
  29. 29.
    W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998) ADSCrossRefGoogle Scholar
  30. 30.
    J. Von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)Google Scholar
  31. 31.
    M. Headrick, Phys. Rev. D 82, 126010 (2010) ADSCrossRefGoogle Scholar
  32. 32.
    D. Frustaglia, K. Richter, Phys. Rev. B 69, 235310 (2004) ADSCrossRefGoogle Scholar
  33. 33.
    M.P. Trushin, A.L. Chudnovskiy, Eur. Phys. J. B 52, 547 (2006)ADSMATHCrossRefGoogle Scholar
  34. 34.
    M.M. Golshan, R. Safaiee, N. Foroozani, J. Comput. Theor. Nanosci. 6, 2235 (2009)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Physics Department, College of SciencesShiraz UniversityShirazIran
  2. 2.Nanotechnology Research InstituteShiraz UniversityShirazIran

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