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Dissipative dynamics of a spin in a spin environment with non-uniform coupling

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Abstract

We investigate the reduced dynamics of a central spin coupled to a spin environment with non-uniform coupling. Through using the method of time-dependent density-matrix renormalization group (t-DMRG), we nonperturbatively show the dissipative dynamics of the central spin beyond the case of uniform coupling between the central spin and the environment spins. It is shown that only when the system-environment coupling is weak enough, the central spin system shows Markovian effect and will finally reach the steady state; otherwise, the reduced dynamics is non-Markovian and exhibits a quasi-periodic oscillation. The frequency spectrum and the correlation between the central spin system and the environment are also studied to elucidate the dissipative dynamics of the central spin system for different coupling strengths.

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References

  1. M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)

  2. T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L. O’Brien, Nature 464, 45 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, J. Vučković, Science 320, 769 (2008)

    Article  ADS  Google Scholar 

  5. D. Press, T.D. Ladd, B.Y. Zhang, Y. Yamamoto, Nature 456, 218 (2008)

    Article  ADS  Google Scholar 

  6. M.V.G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A.S. Zibrov, P.R. Hemmer, M.D. Lukin, Science 316, 1312 (2007)

    Article  Google Scholar 

  7. N. Zhao, Z.Y. Wang, R.B. Liu, Phys. Rev. Lett. 106, 217205 (2011)

    Article  ADS  Google Scholar 

  8. N. Zhao, S.W. Ho, R.B. Liu, Phys. Rev. B 85, 115303 (2012)

    Article  ADS  Google Scholar 

  9. A.J. Leggett, S. Chakravarty, A.T. Dorsey, M.P.A. Fisher, A. Garg, W. Zwerger, Rev. Mod. Phys. 59, 1 (1987)

    Article  ADS  Google Scholar 

  10. U. Weiss, Quantum dissipative systems, 3rd edn. (World Scientific Publishing, 2008)

  11. J.S. Shao, P. Hänggi, Phys. Rev. Lett. 81, 5710 (1998)

    Article  ADS  Google Scholar 

  12. D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, R. Fazio, Phys. Rev. A 75, 032333 (2007)

    Article  ADS  Google Scholar 

  13. N. Makri, D.E. Makarov, J. Chem. Phys. 102, 4600 (1995)

    Article  ADS  Google Scholar 

  14. R. Bulla, T.A. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008)

    Article  ADS  Google Scholar 

  15. R. Egger, C.H. Mak, Phys. Rev. B 50, 15210 (1994)

    Article  ADS  Google Scholar 

  16. J. Schliemann, A. Khaeskii, D. Loss, J. Phys. B 15, R1809 (2003)

    Google Scholar 

  17. W.A. Coish, D. Loss, Phys. Rev. B 70, 195340 (2004)

    Article  ADS  Google Scholar 

  18. W. Yao, R.B. Liu, L.J. Sham, Phys. Rev. B 74, 195301 (2006)

    Article  ADS  Google Scholar 

  19. F.M. Cucchietti, J.P. Paz, W.H. Zurek, Phys. Rev. A 72, 052113 (2004)

    Article  ADS  Google Scholar 

  20. B. Erbe, J. Schliemann, Phys. Rev. Lett. 105, 177602 (2010)

    Article  ADS  Google Scholar 

  21. E. Ferraro, H.P. Breuer, A. Napoli, A. Messina, Phys. Scr. T140, 014021 (2010)

    Article  ADS  Google Scholar 

  22. W.M. Witzel, M.S. Carroll, L. Cywinski, S.D. Sarma, Phys. Rev. B 86, 035452 (2012)

    Article  ADS  Google Scholar 

  23. E. Barnes, L. Cywinski, S.D. Sarma, Phys. Rev. Lett. 109, 140403 (2012)

    Article  ADS  Google Scholar 

  24. H.P. Breuer, D. Burgarth, F. Petruccione, Phys. Rev. B 70, 045323 (2004)

    Article  ADS  Google Scholar 

  25. Y. Hamdouni, M. Fannes, F. Petruccione, Phys. Rev. B 73, 245323 (2006)

    Article  ADS  Google Scholar 

  26. A. Hutton, S. Bose, Phys. Rev. A 69, 042312 (2004)

    Article  ADS  Google Scholar 

  27. H.P. Breuer, F. Petruccione, Phys. Rev. E 76, 016701 (2007)

    Article  ADS  Google Scholar 

  28. X.Z. Yuan, H.S. Goan, K.D. Zhu, New J. Phys. 13, 023018 (2011)

    Article  ADS  Google Scholar 

  29. Y. Hamdouni, J. Phys. A 42, 315301 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  30. H.T. Quan, Z. Song, X.F. Liu, P. Zanardi, C.P. Sun, Phys. Rev. Lett. 96, 140604 (2006)

    Article  ADS  Google Scholar 

  31. M. Bortz, J. Stolze, Phys. Rev. B 76, 014304 (2007)

    Article  ADS  Google Scholar 

  32. Y.Y. Tian, P.C. Chen, D.W. Wang, Phys. Rev. B 77, 174434 (2008)

    Article  ADS  Google Scholar 

  33. H.F. Wang, S. Ashhab, F. Nori, Phys. Rev. A 83, 062317 (2011)

    Article  ADS  Google Scholar 

  34. C.Y. Lai, J.T. Hung, C.Y. Mou, P.C. Chen, Phys. Rev. B 77, 205419 (2008)

    Article  ADS  Google Scholar 

  35. G. Vidal, Phys. Rev. Lett. 93, 040502 (2004)

    Article  ADS  Google Scholar 

  36. S. White, A. Feiguin, Phys. Rev. Lett. 93, 076401 (2004)

    Article  ADS  Google Scholar 

  37. V. Vedral, Rev. Mod. Phys. 74, 197 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  38. Z.H. Wang, Y. Guo, D.L. Zhou, Eur. Phys. J. D 67, 218 (2013)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Physics and Electronic Science, Changsha University of Science and Technology, Changsha, 410004, P.R. China

    Y. Guo

  2. Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Z. H. Wang & D. L. Zhou

Authors
  1. Y. Guo
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  2. Z. H. Wang
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  3. D. L. Zhou
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Correspondence to Y. Guo.

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Guo, Y., Wang, Z.H. & Zhou, D.L. Dissipative dynamics of a spin in a spin environment with non-uniform coupling. Eur. Phys. J. D 68, 110 (2014). https://doi.org/10.1140/epjd/e2014-40597-5

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  • DOI: https://doi.org/10.1140/epjd/e2014-40597-5

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