Skip to main content
Log in

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

  • Regular Article
  • Mesoscopic and Nanoscale Systems
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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)

    Article  MATH  Google Scholar 

  2. D. Loss, G. Burkard, D.P. DiVincenzo, J. Nanopart. Res. 2, 401 (2000)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  4. D. Stepanenko, N.E. Bonesteel, Phys. Rev. Lett. 93, 140501 (2004)

    Article  ADS  Google Scholar 

  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 therein

    Article  ADS  Google Scholar 

  6. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Y. Zhou, G.-F. Zhang, Eur. Phys. J. D 47, 227 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. G. Burkard, D. Loss, D.P. DiVincenzo, Phys. Rev. B 59, 2070 (1999)

    Article  ADS  Google Scholar 

  10. G. Burkard, H.-A. Engel, D. Loss, Fortschr. Phys. 48, 965 (2000)

    Article  Google Scholar 

  11. J. Schliemann, D. Loss, A.H. MacDonald, Phys. Rev. B 63, 085311 (2001)

    Article  ADS  Google Scholar 

  12. A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, K. Peng, Phys. Rev. A 78, 013828 (2008)

    Article  ADS  Google Scholar 

  13. P.C. Haljan, K.-A. Brickman, L. Deslauriers, P.J. Lee, C. Monroe, Phys. Rev. Lett. 94, 153602 (2005)

    Article  ADS  Google Scholar 

  14. M.S. Sherwin, A. Imamoglu, T. Montroy, Phys. Rev. A 60, 3508 (1999)

    Article  ADS  Google Scholar 

  15. T.B. Pittman, J.D. Franson, Phys. Rev. A 66, 062302 (2002)

    Article  ADS  Google Scholar 

  16. V. Corato, C. Granata, S. Rombetto, B. Ruggiero, M. Russo, R. Russo, P. Silvestrini, A. Vettoliere, IEEE Trans. Appl. Supercond. 17, 132 (2007)

    Article  ADS  Google Scholar 

  17. T. Koga, J. Nitta, M. van Veenhuizen, Phys. Rev. B 70, R161302 (2004)

    Article  ADS  Google Scholar 

  18. Y.A. Bychkov, E.I. Rashba, J. Phys. C 17, 6039 (1984)

    Article  ADS  Google Scholar 

  19. P. Stano, Ph. D. thesis, University of Regensburg, 2007

  20. M. Trushin, Ph. D. thesis, University of Hamburg, 2005

  21. M.J. Yang, C.H. Yang, Y.B. Lyanda-Geller, Physica E 22, 304 (2004)

    Article  ADS  Google Scholar 

  22. M.J. Yang, C.H. Yang, Y.B. Lyanda-Geller, Europhys. Lett. 66, 826 (2004)

    Article  ADS  Google Scholar 

  23. M.P. Trushin, A.L. Chudnovskiy, Eur. Phys. J. B 52, 547 (2006)

    Article  ADS  MATH  Google Scholar 

  24. M.P. Trushin, A.L. Chudnovskiy, Physica E 34, 397 (2006)

    Article  ADS  Google Scholar 

  25. S. Debald, C. Emary, Phys. Rev. Lett. 94, 226803 (2005)

    Article  ADS  Google Scholar 

  26. B.K. Nikolić, S. Souma, Phys. Rev. B 71, 195328 (2005)

    Article  ADS  Google Scholar 

  27. R. Safaiee, M.M. Golshan, N. Foroozani, J. Stat. Mech. P11014, (2009)

  28. E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. J. Von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)

  31. M. Headrick, Phys. Rev. D 82, 126010 (2010)

    Article  ADS  Google Scholar 

  32. D. Frustaglia, K. Richter, Phys. Rev. B 69, 235310 (2004)

    Article  ADS  Google Scholar 

  33. M.P. Trushin, A.L. Chudnovskiy, Eur. Phys. J. B 52, 547 (2006)

    Article  ADS  MATH  Google Scholar 

  34. M.M. Golshan, R. Safaiee, N. Foroozani, J. Comput. Theor. Nanosci. 6, 2235 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Safaiee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Safaiee, R., Golshan, M.M. Entanglement of electronic subbands and coherent superposition of spin states in a Rashba nanoloop. Eur. Phys. J. B 83, 457–463 (2011). https://doi.org/10.1140/epjb/e2011-20142-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2011-20142-x

Keywords

Navigation