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The Zeno effect and relaxation rates in a triple quantum dot system

  • Xue-Ning HuEmail author
  • Hong Jiang
  • Chao Zhang
Regular Article
  • 50 Downloads

Abstract

We study the quantum Zeno effect (QZE) and relaxation rates in a three quantum dot system with a mesoscopic detector near one of the three dots. The evolution of three dot states is analyzed under different conditions. For small energy differences, we find that quantum anti-Zeno effect (QAZE) occurs because measurements cannot localize the electron in the initial dot state at arbitrary voltage or temperature, but accelerate quantum transition of the electron. For large energy gaps, dot states remain the initial values, namely, Zeno effect occurs. With increasing voltage or temperature, the relaxation rates which are related to quantum transition between eigenstates increase. Furthermore, it is demonstrated that they are not absolutely dependent on the eigen energy and the difference of eigen energy. The voltage and temperature play a similar role on the relaxation rates, but a different role on occupation probabilities. In addition, it is proved that the voltage induces relaxation at zero temperature. Moreover, we demonstrate that the change rates of occupation probabilities under eigenstate and dot state are related to the energy differences. In both dot-state and eigenstate representations, the first derivatives of occupation probabilities versus voltage change obviously when the voltage is matched with the difference of eigen energy (We use the unit system of e = kB = = 1), but the first derivatives of occupation probabilities versus temperature change obviously when the temperature is matched with the difference of dot-state energy. Especially, for large energy gaps, the first derivatives of occupation probabilities versus voltage change rapidly when the voltage is matched with the difference of dot-state energy. The temperatures, at which the first derivatives of occupation probabilities versus temperature change rapidly, are independent of the differences of both dot-state and eigen energy.

Graphical abstract

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    S. Bednarek, B. Szafran, R.J. Dudek, K. Lis, Phys. Rev. Lett. 100, 126805 (2008) ADSCrossRefGoogle Scholar
  2. 2.
    F. Delgado, J. Fernández-Rossier, Phys. Rev. Lett. 108, 196602 (2012) ADSCrossRefGoogle Scholar
  3. 3.
    S. Saito, X. Zhu, R. Amsüss, Y. Matsuzaki, K. Kakuyanagi, T. Shimo-Oka, N. Mizuochi, K. Nemoto, W.J. Munro, K. Semba, Phys. Rev. Lett. 111, 107008-1-5 (2012) ADSGoogle Scholar
  4. 4.
    N. Kalb, A. Reiserer, S. Ritter, G. Rempe, Phys. Rev. Lett. 114, 220501 (2015) ADSCrossRefGoogle Scholar
  5. 5.
    I. Neder, M. Heiblum, D. Mahalu, V. Umansky, Phys. Rev. Lett. 98, 036803 (2007) ADSCrossRefGoogle Scholar
  6. 6.
    K.S. Choi, H. Deng, J. Laurat et al., Nature 452, 67 (2008) ADSCrossRefGoogle Scholar
  7. 7.
    J.L. de Oliveira, D.S. Oliveira, R.V. Ramos, Quantum Inf. Process. 11, 255 (2012) CrossRefGoogle Scholar
  8. 8.
    E. Onac, F. Balestro, L.H. Willems van Beveren, U. Hartmann, Y.V. Nazarov, L.P. Kouwenhoven, Phys. Rev. Lett. 96, 176601 (2006) ADSCrossRefGoogle Scholar
  9. 9.
    N. Erez, G. Gordon, M. Nest, G. Kurizki, Nature 452, 724 (2008) ADSCrossRefGoogle Scholar
  10. 10.
    D. Sokolovski, S.A. Gurvitz, Phys. Rev. A 79, 032106 (2006) ADSCrossRefGoogle Scholar
  11. 11.
    G.G. Gillett, R.B. Dalton, B.P. Lanyon, M.P. Almeida, M. Barbieri, G.J. Pryde, J.L. O’Brien, K.J. Resch, S.D. Bartlett, A.G. White, Phys. Rev. Lett. 104, 080503 (2010) ADSCrossRefGoogle Scholar
  12. 12.
    A. Hentschel, B.C. Sanders, Phys. Rev. Lett. 104, 063603 (2010) ADSCrossRefGoogle Scholar
  13. 13.
    J.Z. Bernád, M. Jääskeläinen, U. Zülicke, Phys. Rev. B 81, 073403 (2010) ADSCrossRefGoogle Scholar
  14. 14.
    T.C. Ralph, Quantum Inf. Process. 11, 313 (2012) CrossRefGoogle Scholar
  15. 15.
    J.M. Elzerman, R. Hanson, L.H. Willems van Beveren, B. Witkamp, L.M.K. Vandersypen, L.P. Kouwenhoven, Nature 430, 431 (2004) ADSCrossRefGoogle Scholar
  16. 16.
    S. Sasaki, T. Fujisawa, T. Hayashi, Y. Hirayama, Phys. Rev. Lett. 95, 056803 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    J.R. Petta, A.C. Johnson, A. Yacoby, C.M. Marcus, M.P. Hanson, A.C. Gossard, Phys. Rev. B 72, 161301 (2005) ADSCrossRefGoogle Scholar
  18. 18.
    T. Meunier, I.T. Vink, L.H. Willems van Beveren, K.-J. Tielrooij, R. Hanson, F.H.L. Koppens, H.P. Tranitz, W. Wegscheider, L.P. Kouwenhoven, L.M.K. Vandersypen, Phys. Rev. Lett. 98, 126601 (2007) ADSCrossRefGoogle Scholar
  19. 19.
    S. Amasha, K. MacLean, I.P. Radu, D.M. Zumbühl, M.A. Kastner, M.P. Hanson, A.C. Gossard, Phys. Rev. Lett. 100, 046803 (2008) ADSCrossRefGoogle Scholar
  20. 20.
    W.M. Itano, D.J. Heinzen, J.J. Bollinger, D.J. Wineland, Phys. Rev. A 41, 2295 (1990) ADSCrossRefGoogle Scholar
  21. 21.
    E. Block, P.R. Berman, Phys. Rev. A 44, 1466 (1991) ADSCrossRefGoogle Scholar
  22. 22.
    L.S. Schulman, Phys. Rev. A 57, 1509 (1998) ADSCrossRefGoogle Scholar
  23. 23.
    G.S. Agarwal, S.P. Tewari, Phys. Lett. A 185, 139 (1994) ADSCrossRefGoogle Scholar
  24. 24.
    A.G. Kofman, G. Kurizki, Phys. Rev. A 54, R3750 (1996) ADSCrossRefGoogle Scholar
  25. 25.
    S.A. Gurvitz, Phys. Rev. B 56, 15215 (1997) ADSCrossRefGoogle Scholar
  26. 26.
    G. Hackenbroich, B. Rosenow, H.A. Weidenmüller, Phys. Rev. Lett. 81, 5896 (1998) ADSCrossRefGoogle Scholar
  27. 27.
    B. Elattari, S.A. Gurvitz, Phys. Rev. A 62, 032102 (2000) ADSCrossRefGoogle Scholar
  28. 28.
    B. Elattari, S.A. Gurvitz, Phys. Rev. Lett. 84, 2047 (2000) ADSCrossRefGoogle Scholar
  29. 29.
    P.-W. Chen, D.-B. Tsai, P. Bennett, Phys. Rev. B 81, 115307 (2010) ADSCrossRefGoogle Scholar
  30. 30.
    L.T. Xu, Y.S. Cao, X.Q. Li, Phys. Rev. A 90, 022108 (2014) ADSCrossRefGoogle Scholar
  31. 31.
    B. Kaulakys, V. Gontis, Phys. Rev. A 56, 1131 (1997) ADSCrossRefGoogle Scholar
  32. 32.
    A.G. Kofman, G. Kurizki, Nature 405, 546 (2000) ADSCrossRefGoogle Scholar
  33. 33.
    P. Facchi, H. Nakazato, S. Pascazio, Phys. Rev. Lett. 86, 2699 (2001) ADSCrossRefGoogle Scholar
  34. 34.
    K. Thapliyal, A. Pathak, J. Peřina, Phys. Rev. A 93, 022107 (2016) ADSCrossRefGoogle Scholar
  35. 35.
    P.G. Kwiat, A.G. White, J.R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, A. Zeilinger, Phys. Rev. Lett. 83, 4725 (1999) ADSCrossRefGoogle Scholar
  36. 36.
    M.C. Fischer, B. Gutiérrez-Medina, M.G. Raizen, Phys. Rev. Lett. 87, 040402 (2001) ADSCrossRefGoogle Scholar
  37. 37.
    H. Zheng, S.Y. Zhu, M.S. Zubairy, Phys. Rev. Lett. 101, 200404 (2008) ADSCrossRefGoogle Scholar
  38. 38.
    Q. Ai, Y. Li, H. Zheng, C.P. Sun, Phys. Rev. A 81, 042116 (2010) ADSCrossRefGoogle Scholar
  39. 39.
    S.A. Gurvitz, Phys. Rev. Lett. 91, 066801 (2003) ADSCrossRefGoogle Scholar
  40. 40.
    S.A. Gurvitz, Phys. Rev. B 77, 075325 (2008) ADSCrossRefGoogle Scholar
  41. 41.
    X.N. Hu, X.Q. Li, Phys. Rev. B 73, 035320 (2006) ADSCrossRefGoogle Scholar
  42. 42.
    X.N. Hu, C.S. Zhang, Z.H. Dai, Physica B 416, 51 (2013) ADSCrossRefGoogle Scholar
  43. 43.
    X.Q. Li, W.K. Zhang, P. Cui, J.S. Shao, Z.S. Ma, Y.J. Yan, Phys. Rev. B 69, 085315 (2004) ADSCrossRefGoogle Scholar
  44. 44.
    R.X. Xu, Y.J. Yan, X.Q. Li, Phys. Rev. A 65, 023807 (2002) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Science and Technology for Opto-electronic Information, YanTai UniversityShandongP.R. China

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