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Entanglement of magnetic impurities through electron scattering in an electric field

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Abstract

We show that the entanglement between two distant magnetic impurities, generated via electron scattering, can be easily modulated by controlling the magnitude of an applied external electric field. We assume that the two magnetic impurities are fixed and located on an one-dimensional quantum wire. A ballistic electron moving through the wire is scattered off by both impurities, so the electron spin can be seen as a mediator between the spins of the impurities. Heisenberg operators are used to describe the interactions between electron and impurities spins. We use a wave guide formalism to model the ballistic electron wave function. Entanglement control is shown to be possible for three different protocols of entanglement detection. The effect of detection protocols on the entanglement extraction is discussed.

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References

  1. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Yamamoto, M., Takada, S., Baeuerle, C., Watanabe, K., Wieck, A.D., Tarucha, S.: Electrical control of a solid-state flying qubit. Nat. Nanotechnol. 7, 247 (2012)

    Article  ADS  Google Scholar 

  3. Chen, G.Y., Lambert, N., Chou, C.H., Chen, Y.N., Nori, F.: Surface plasmons in a metal nanowire coupled to colloidal quantum dots: scattering properties and quantum entanglement. Phys. Rev. B 84, 045310 (2011)

    Article  ADS  Google Scholar 

  4. Popescu, A.E., Ionicioiu, R.: All-electrical quantum computation with mobile spin qubits. Phys. Rev. B 69, 245422 (2004)

    Article  ADS  Google Scholar 

  5. Cirac, J.I., Zoller, P., Kimble, H.J., Mabuchi, H.: Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221 (1997)

    Article  ADS  Google Scholar 

  6. Yao, W., Liu, R.B., Sham, L.J.: Theory of control of the spin-photon interface for quantum networks. Phys. Rev. Lett. 95, 030504 (2005)

    Article  ADS  Google Scholar 

  7. Tanzilli, S., Tittel, W., Halder, M., Alibart, O., Baldi, P., Gisin, N., Zbinden, H.: A photonic quantum information interface. Nature 437, 116 (2005)

    Article  ADS  Google Scholar 

  8. Cho, S.Y., McKenzie, R.H.: Quantum entanglement in the two-impurity Kondo model. Phys. Rev. A 73, 012109 (2006)

    Article  ADS  Google Scholar 

  9. Nizama, M., Frustaglia, D., Hallberg, K.: Quantum correlations in nanostructured two-impurity Kondo systems. Phys. Rev. B 86, 075413 (2012)

    Article  ADS  Google Scholar 

  10. Bayat, A., Bose, S., Sodano, P., Johannesson, H.: Entanglement probe of two-impurity Kondo physics in a spin chain. Phys. Rev. Lett. 109, 066403 (2012)

    Article  ADS  Google Scholar 

  11. Bayat, A., Johannesson, H., Bose, S., Sodano, : An order parameter for impurity systems at quantum criticality. Nat. Commun. 5, 3784 (2014)

    Article  ADS  Google Scholar 

  12. Kikkawa, J.M., Awschalom, D.D.: Lateral drag of spin coherence in gallium arsenide. Nature 397, 139 (1999)

    Article  ADS  Google Scholar 

  13. Chen, W., Shen, R., Wang, Z.D., Sheng, L., Wang, B.G., Xing, D.Y.: Quantitatively probing two-electron entanglement with a spintronic quantum eraser. Phys. Rev. B 87, 155308 (2013)

    Article  ADS  Google Scholar 

  14. Fuchs, M., Rychkov, V., Trauzettel, B.: Spin decoherence in graphene quantum dots due to hyperfine interaction. Phys. Rev. B 86, 085301 (2012)

    Article  ADS  Google Scholar 

  15. Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: The electronic properties of graphene. Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  16. Feve, G., Mahe, A., Berroir, J.M., Kontos, T., Placais, B., Glattli, D.C., Cavanna, A., Etienne, B., Jin, Y.: An on-demand coherent single-electron source. Science 316, 1169 (2007)

    Article  ADS  Google Scholar 

  17. Hermelin, S., Takada, S., Yamamoto, M., Tarucha, S., Wieck, A.D., Saminadayar, L., Bauerle, C., Meunier, T.: Electrons surfing on a sound wave as a platform for quantum optics with flying electrons. Nature 477, 435 (2011)

    Article  ADS  Google Scholar 

  18. McNeil, R.P.G., Kataoka, M., Ford, C.J.B., Barnes, C.H.W., Anderson, D., Jones, G.A.C., Farrer, I., Ritchie, D.A.: On-demand single-electron transfer between distant quantum dots. Nature 477, 439 (2011)

    Article  ADS  Google Scholar 

  19. Cordourier-Maruri, G., Ciccarello, F., Omar, Y., Zarcone, M., de Coss, R., Bose, S.: Implementing quantum gates through scattering between a static and a flying qubit. Phys. Rev. A 82, 052313 (2010)

    Article  ADS  Google Scholar 

  20. 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 

  21. Ciccarello, F., Bose, S., Zarcone, M.: Teleportation between distant qudits via scattering of mobile qubits. Phys. Rev. A 81, 042318 (2010)

    Article  ADS  Google Scholar 

  22. 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 

  23. Ciccarello, F., Palma, G.M., Zarcone, M., Omar, Y., Vieira, V.R.: Entanglement controlled single-electron transmittivity. New J. Phys. 8, 214 (2006)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Ciccarello, F., Palma, G.M., Zarcone, M., Omar, Y., Vieira, V.R.: Electron Fabry–Perot interferometer with two entangled magnetic impurities. J. Phys. A Math. Theor. 40, 7993 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  27. Metavitsiadis, A., Dillenschneider, R., Eggert, S.: Impurity entanglement through electron scattering in a magnetic field. Phys. Rev. B 89, 155406 (2014)

    Article  ADS  Google Scholar 

  28. Ciccarello, F., Browne, D.E., Kwek, L.C., Schomerus, H., Zarcone, M., Bose, S.: Quasideterministic realization of a universal quantum gate in a single scattering process. Phys. Rev. A 85, 050305(R) (2012)

    Article  ADS  Google Scholar 

  29. White, C.T., Todorov, T.N.: Carbon nanotubes as long ballistic conductors. Nature 393, 240 (1998)

    Article  ADS  Google Scholar 

  30. Balents, L., Egger, R.: Spin transport in interacting quantum wires and carbon nanotubes. Phys. Rev. Lett. 85, 3464 (2000)

    Article  ADS  Google Scholar 

  31. Gunlycke, D., Jefferson, J.H., Rejec, T., Ramsak, A., Pettifor, D.G., Briggs, G.A.: Entanglement between static and flying qubits in a semiconducting carbon nanotube. J. Phys. Condens. Matter 18, 851 (2006)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  33. Auslaender, O.M., Yacoby, A., de Picciotto, R., Baldwin, Kw, Pfeiffer, L.N., West, K.W.: Experimental evidence for resonant tunneling in a Luttinger liquid. Phys. Rev. Lett. 84, 1764 (2000)

    Article  ADS  Google Scholar 

  34. 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 

  35. Allen, S.S., Richardson, S.L.: Theoretical investigations of resonant-tunneling in asymmetric multibarrier semiconductor heterostructures in an applied constant electric-field. Phys. Rev. B 50, 11693 (1994)

  36. Miyamoto, K., Yamamoto, H.: Resonant tunneling in asymmetrical double-barrier structures under an applied electric field. J. Appl. Phys. 84, 311 (1998)

    Article  ADS  Google Scholar 

  37. Ming, Y., Gong, J., Zhang, R.Q.: Spin-polarized transport through ZnMnSe/ZnSe/ZnBeSe heterostructures. J. Appl. Phys. 110, 093717 (2011)

    Article  ADS  Google Scholar 

  38. Bu, X., Wang, J., Shi, J., Zhao, H.: Research on the electronic tunneling in asymmetric dual-quantum-well. Adv. Mater. Res. 542, 953 (2014)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Field, M., Smith, C.G., Pepper, M., Ritchie, D.A., Frost, J.E.F., Jones, G.A.C., Hasko, D.G.: Measurements of coulomb blockade with noninvasive voltage probe. Phys. Rev. Lett. 70, 1311 (1993)

    Article  ADS  Google Scholar 

  41. Meier, f, Bona, G.L., Hüfner, S.: Experimental-determination of exchange constants by spin-polarized photoemission. Phys. Rev. Lett. 52, 1152 (1984)

    Article  ADS  Google Scholar 

  42. Cordourier-Maruri, G., Gupta, V., de Coss, R.: Recurrence in resonant transmission of the one-dimensional array of delta potentials. Mod. Phys. Lett. B 28, 1450016 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

GCM acknowledge to Consejo Nacional de Ciencia y Tecnología (Conacyt, México) for a postdoctoral grant. This research was partially funded by Conacyt, México, Under Grant No. 83604.

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Authors and Affiliations

  1. Facultad de Ingeniería, Universidad Autónoma de Yucatán, A.P. 150 Cordemex, 97310, Mérida, Yucatán, Mexico

    Oscar Lazo-Arjona

  2. Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK

    Guillermo Cordourier-Maruri

  3. Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, A.P. 73 Cordemex, 97310, Mérida, Yucatán, Mexico

    Guillermo Cordourier-Maruri & Romeo de Coss

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  1. Oscar Lazo-Arjona
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  2. Guillermo Cordourier-Maruri
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  3. Romeo de Coss
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Correspondence to Guillermo Cordourier-Maruri.

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Lazo-Arjona, O., Cordourier-Maruri, G. & de Coss, R. Entanglement of magnetic impurities through electron scattering in an electric field. Quantum Inf Process 14, 3757–3772 (2015). https://doi.org/10.1007/s11128-015-1062-5

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  • DOI: https://doi.org/10.1007/s11128-015-1062-5

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