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Entanglement generation due to the Klein tunneling in a graphene sheet

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Abstract

Scattering of a ballistic electron by the quantum-dot spin qubits fixed in a graphene nanoribbon is investigated theoretically. Two simple cases are investigated in details: scattering from a static quantum dot and scattering from two static quantum dots located at a fixed distance from each other. For the first case, it is shown that the Klein tunneling in a graphene sheet leads to a final entangled state for the reflected and/or transmitted electrons. The amount of the generated entanglement through the scattering process is a function of the incident angle for the ballistic electrons. For the second case, it is shown that the created correlation between the quantum dots is a periodic function of their distance. For frontal incident electrons in both cases, there is not any reflection and the Klein tunneling effect leads to a final well-correlated state for the scattering system.

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References

  1. Meyer, J.C., Geim, A.K., Katsnelson, M.I., Novoselov, K.S., Booth, T.J., Roth, S.: The structure of suspended graphene sheets. Nature 446, 7131 (2007)

    Google Scholar 

  2. Geim, A.K.: Graphene: status and prospects. Science 324, 1530 (2009)

    Article  ADS  Google Scholar 

  3. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A.: Electric field effect in atomically thin carbon films. Science 306, 666 (2004)

    Article  ADS  Google Scholar 

  4. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A.: Two-dimensional gas of massless Dirac fermions in graphene. Nature (London) 438, 197 (2005)

    Article  ADS  Google Scholar 

  5. Berger, C., Song, Z., Li, T., Li, X., Ogbazghi, A.Y., Feng, R., Dai, Z., Marchenkov, A.N., Conrad, E.H., First, P.N., de Heer, W.A.: Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B. 108, 19912 (2004)

    Article  Google Scholar 

  6. Klein, O.: Die reflexion von elektronen an einem potentialsprung nach der relativistischen dynamik von Dirac. Z. Phys. 53, 157 (1929)

    Article  ADS  MATH  Google Scholar 

  7. Katsnelson, M.I., Novoselov, K.S., Geim, A.K.: Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2, 620 (2006)

    Article  Google Scholar 

  8. Beenakker, C.W.J.: Colloquium: Andreev reflection and Klein tunneling in graphene. Rev. Mod. Phys. 80, 1337 (2008)

    Article  ADS  Google Scholar 

  9. Stander, N., Huard, B., Goldhaber-Gordon, D.: Evidence for Klein tunneling in graphene p–n junctions. Phys. Rev. Lett. 102, 026807 (2009)

    Article  ADS  Google Scholar 

  10. Young, A.F., Kim, P.: Quantum interference and Klein tunnelling in graphene heterojunctions. Nat. Phys. 5, 222 (2009)

    Article  Google Scholar 

  11. Dombey, N., Calogeracos, A.: Seventy years of the Klein paradox. Phys. Rep. 315, 41 (1999)

    Article  ADS  MATH  Google Scholar 

  12. Allain, P.E., Fuchs, J.N.: Klein tunneling in graphene: optics with massless electrons. Eur. Phys. J. B. 83, 301 (2011)

    Article  ADS  Google Scholar 

  13. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1953)

    Article  ADS  MATH  Google Scholar 

  14. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Costa Jr., A.T., Bose, S., Omar, Y.: Entanglement of two impurities through electron scattering. Phys. Rev. Lett. 96, 230501 (2006)

    Article  ADS  Google Scholar 

  17. Hida, Y., Nakazato, H., Yuasa, K., Omar, Y.: Entanglement generation by qubit scattering in three dimensions. Phys. Rev. A 80, 012310 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  18. Yuasa, K., Nakazato, H.: Resonant scattering can enhance the degree of entanglement. J. Phys. A: Math. Theor. 40, 297 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Ghanbari-Adivi, E., Soltani, M., Ebtekarnasab, H.: Entanglement generation in scattering of particles from spin impurities. Eur. Phys. J. D 67, 118 (2013)

    Article  ADS  MATH  Google Scholar 

  20. Ghanbari-Adivi, E., Soltani, M., Ebtekarnasab, H.: Entanglement production in scattering of Gaussian wave packets from fixed localized impurities. Eur. Phys. J. D 68, 103 (2014)

    Article  ADS  MATH  Google Scholar 

  21. Ghanbari-Adivi, E., Soltani, M.: Entanglement generation between two colliding particles. Eur. Phys. J. D 68, 336 (2014)

    Article  ADS  Google Scholar 

  22. Ghanbari-Adivi, E., Soltani, M., Sheikhali, M.N.: Entanglement and quantum discord creation in different setups of a one-dimensional scattering experiment. Eur. Phys. J. D 69, 179 (2015)

    Article  ADS  Google Scholar 

  23. Cordourier-Maruri, G., Omar, Y., de Coss, R., Bose, S.: Graphene-enabled low-control quantum gates between static and mobile spins. Phys. Rev. B 89, 075426 (2014)

    Article  ADS  Google Scholar 

  24. Trauzettel, B., Bulaev, D.V., Loss, D., Burkard, G.: Spin qubits in graphene quantum dots. Nat. Phys. 3, 192 (2007)

    Article  Google Scholar 

  25. Yan, J., Thygesen, K.S., Jacobsen, K.W.: Nonlocal screening of plasmons in graphene by semiconducting and metallic substrates: first-principles calculations. Phys. Rev. Lett. 106, 146803 (2011)

    Article  ADS  Google Scholar 

  26. Bena, C., Montambaux, G.: Remarks on the tight-binding model of graphene. New J. Phys. 11, 095003 (2009)

    Article  ADS  Google Scholar 

  27. Gunlycke, D., Jefferson, J.H., Rejec, T., Ramsak, A., Pettifor, D.G., Briggs, G.A.D.: Entanglement between static and flying qubits in a semiconducting carbon nanotube. J. Phys.: Condens. Matter 18, S851 (2006)

    ADS  Google Scholar 

  28. Lazo-Arjona, O., Cordourier-Maruri, G., de Coss, R.: Entanglement of magnetic impurities through electron scattering in an electric field. Quantum Inf. Process. 14, 3757 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  30. Fowles, G.R.: Introduction to Modern Optics. Dover, New York (2012)

    Google Scholar 

  31. Reitz, J.R., Milford, F.J., Christy, R.W.: Foundations of Electromagnetic Theory. Addison-Wesley, New York (2009)

    MATH  Google Scholar 

  32. Cordourier-Maruri, G., de Coss, R., Gupta, V.: Transmission properties of the one-dimensional array of delta potentials. Mod. Phys. Lett. B 25, 1349 (2011)

    Article  ADS  MATH  Google Scholar 

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Acknowledgments

One of the authors, M. Sheikhali, would like to acknowledge the office of graduate studies at the University of Isfahan for their support and research facilities.

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Authors and Affiliations

  1. Department of Physics, Faculty of Sciences, University of Isfahan, Isfahan, 81746-73441, Iran

    E. Ghanbari-Adivi, M. Soltani & M. Sheikhali

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  1. E. Ghanbari-Adivi
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  2. M. Soltani
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  3. M. Sheikhali
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Correspondence to E. Ghanbari-Adivi.

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Ghanbari-Adivi, E., Soltani, M. & Sheikhali, M. Entanglement generation due to the Klein tunneling in a graphene sheet. Quantum Inf Process 15, 2377–2391 (2016). https://doi.org/10.1007/s11128-016-1280-5

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  • DOI: https://doi.org/10.1007/s11128-016-1280-5

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