Skip to main content

Postselective measurement of the electronic entanglement in the system of two Mach-Zehnder interferometers with coulomb interaction

Abstract

The parameters at which the maximally entangled two-particle state appears in the system of two ideal electronic Mach-Zehnder interferometers are known. In this work, the operation of nonideal devices with finite scattering in splitters and with reflection in the region of the Coulomb Interaction has been considered. It has been shown that, under the condition of postselection of experimental results, these factors can increase the observed Bell parameter to values exceeding Cirel’son’s (or Tsirelson’s) bound equal to 2√2 up to the mathematical limit equal to 4. A simple postselective measurement scheme providing B = 4 has been described. Although the results of such measurements are not as fundamental as the observation of the violation of Bell’s inequality, they can indirectly indicate the existence of an entangled state in the system. The measurement system is more stable against fluctuations of the phase than a system without postselection. Furthermore, it has been found that the proposed system is optimal for investigation of cross correlations between interferometers in the dc regime (beyond the paradigm of the violation of Bell’s inequality) because they cannot be generated by coordinated fluctuations of Aharonov-Bohm phases.

This is a preview of subscription content, access via your institution.

References

  1. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

    ADS  Article  MATH  Google Scholar 

  2. E. Shrodinger, Naturwissensch. 23, 807 (1935).

    ADS  Article  Google Scholar 

  3. J. S. Bell, Phys. 1, 195 (1964).

    Google Scholar 

  4. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

    ADS  Article  Google Scholar 

  5. B. Tsirelson, Lett. Math. Phys. 4, 93 (1980).

    ADS  Article  MathSciNet  Google Scholar 

  6. A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 49, 91 (1982).

    ADS  Article  Google Scholar 

  7. G. Lesovik, T. Martin, and G. Blatter, Eur. Phys. J. B 24, 287 (2001).

    ADS  Article  Google Scholar 

  8. P. Recher, E. Sukhorukov, and D. Loss, Phys. Rev. B 63, 165314 (2001).

    ADS  Article  Google Scholar 

  9. L. Hofstetter, S. Csonka, J. Nygard, and C. Schönenberger, Nature 461, 960 (2009); J. Wei and V. Chandrasekhar, Nature Phys. 6, 494 (2010); A. Das, Y. Ronen, M. Heiblum, et al., Nature Commun. 3, 1165 (2012).

    ADS  Article  Google Scholar 

  10. Y. Ji, Y. Chung, D. Sprinzak, et al., Nature 422, 415 (2003).

    ADS  Article  Google Scholar 

  11. P. Roulleau, F. Portier, D. C. Glattli, et al., Phys. Rev. B 76, 161309 (2007).

    ADS  Article  Google Scholar 

  12. I. Neder, N. Ofek, Y. Chung, et al., Nature 448, 333 (2007).

    ADS  Article  Google Scholar 

  13. I. Neder, M. Heiblum, D. Mahalu, and V. Umansky, Phys. Rev. Lett. 98, 036803 (2007).

    ADS  Article  Google Scholar 

  14. C. W. J. Beenakker, C. Emary, M. Kindermann, and I. L. van Velsen, Phys. Rev. Lett. 91, 147901 (2003).

    ADS  Article  Google Scholar 

  15. P. Samuelsson, E. V. Sukhorukov, and M. Büttiker, Phys. Rev. Lett. 91, 157002 (2003); Phys. Rev. Lett. 92, 026805 (2004).

    ADS  Article  Google Scholar 

  16. K. Kang and K. H. Lee, Physica E 40, 1395 (2008).

    ADS  Article  Google Scholar 

  17. J. Dressel, Y. Choi, and A. N. Jordan, Phys. Rev. B 85, 045320 (2012).

    Article  Google Scholar 

  18. A. A. Vyshnevyy, G. B. Lesovik, and T. Martin, Phys. Rev. B 87, 165417 (2013).

    ADS  Article  Google Scholar 

  19. L. S. Levitov, H. Lee, and G. B. Lesovik, J. Math. Phys. 37, 4845 (1996).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  20. A. V. Lebedev, G. B. Lesovik, and G. Blatter, Phys. Rev. B 72, 245314 (2005).

    ADS  Article  Google Scholar 

  21. J. Keeling, I. Klich, and L. S. Levitov, Phys. Rev. Lett. 97, 116403 (2006).

    ADS  Article  Google Scholar 

  22. F. Hassler, B. Kung, G. B. Lesovik, and G. Blatter, AIP Conf. Proc. 1134, 113 (2008).

    ADS  Google Scholar 

  23. G. Fève, A. Mahé, J.-M. Berroir, et al., Science 316, 1169 (2007).

    ADS  Article  Google Scholar 

  24. A. A. Vyshnevyy, A. V. Lebedev, G. B. Lesovik, and J. Blatter, Phys. Rev. B 87, 165302 (2013).

    ADS  Article  Google Scholar 

  25. D. W. Berry, H. Jeong, M. Stobinska, and T. C. Ralph, Phys. Rev. A 81, 012109 (2010).

    ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Vishnevyy.

Additional information

Original Russian Text © A.A. Vishnevyy, G.B. Lesovik, 2013, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2013, Vol. 98, No. 8, pp. 565–572.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vishnevyy, A.A., Lesovik, G.B. Postselective measurement of the electronic entanglement in the system of two Mach-Zehnder interferometers with coulomb interaction. Jetp Lett. 98, 507–513 (2013). https://doi.org/10.1134/S0021364013210157

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364013210157

Keywords

  • Entangle State
  • JETP Letter
  • Edge State
  • Zehnder Interferometer
  • Ideal Setup