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Quantum and classical correlations in electron-nuclear spin echo

  • Atoms, Molecules, Optics
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Abstract

The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay and electron spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central-spin model in the high-temperature approximation. The same formulas describe discord in both free induction decay and spin echo although the time and magnetic field dependences are different because of difference in the parameters entering into the formulas. Changes in discord in the presence of the nuclear polarization β I in addition to the electron polarization β S have been calculated. It has been shown that the method of reduction of the density matrix to a two-spin electron-nuclear system provides a qualitatively correct description of pair correlations playing the main role at β S ≈ β I and small times. At large times, such correlations decay and multispin correlations ensuring nonzero mutual information and zero quantum discord become dominant.

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References

  1. E. L. Hahn, Phys. Rev. 80, 580 (1950).

    Article  ADS  MATH  Google Scholar 

  2. K. M. Salikhov, A. G. Semenov, and Yu. D. Tsvetkov, Electron Spin Echo and Its Applications (Nauka, Novosibirsk, 1976) [in Russian].

    Google Scholar 

  3. B. Blyumikh, Principles of Nuclear Magnetic Resonance (Tekhnosfera, Moscow, 2007) [in Russian].

    Google Scholar 

  4. J. Waugh, New NMR Methods in Solid State Physics (Cambridge University Press, Cambridge, 1976; Mir, Moscow, 1978).

    Google Scholar 

  5. R. A. Jalabert and H. M. Pastawski, Phys. Rev. Lett. 86, 2490 (2001).

    Article  ADS  Google Scholar 

  6. K. A. Valiev and A. A. Kokin, Quantum Computers: Hopes and Reality (Regular and Chaotic Dynamics, Moscow, 2001) [in Russian].

    Google Scholar 

  7. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000; Mir, Moscow, 2006).

    MATH  Google Scholar 

  8. J. Preskill, Quantum Information and Computation (California Institute of Technology, Pasadena, California, United States, 1998; Regular and Chaotic Dynamics, Moscow, 2008–2011).

    Google Scholar 

  9. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).

    Article  ADS  Google Scholar 

  10. G. G. Kozlov, J. Exp. Theor. Phys. 105(4), 803 (2007).

    Article  ADS  Google Scholar 

  11. W. M. Witzel, M. S. Carroll, L. Cywinski, and S. D. Sarma, Phys. Rev. B: Condens. Matter 86, 035452 (2012).

    Article  ADS  Google Scholar 

  12. Nan Zhao, Sai-Wah Ho, and Ren-Bao Liu, Phys. Rev. B: Condens. Matter 85, 115303 (2012).

    Article  ADS  Google Scholar 

  13. L. T. Hall, J. H. Cole, and L. C. L. Hollenberg, arXiv:1309.5921.

  14. J. Hackmann and F. B. Anders, Phys. Rev. B: Condens. Matter 89, 045317 (2014).

    Article  ADS  Google Scholar 

  15. J. J. L. Morton and B. W. Lovett, Annu. Rev. Condens. Matter Phys. 2, 189 (2011).

    Article  ADS  Google Scholar 

  16. E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998).

    Article  ADS  Google Scholar 

  17. A. Datta, A. Shaji, and C. M. Caves, Phys. Rev. Lett. 100, 050502 (2008).

    Article  ADS  Google Scholar 

  18. A. F. Fahmy, R. Max, W. Bermel, and S. J. Glasser, Phys. Rev. A: At., Mol., Opt. Phys. 78, 022317 (2008).

    Article  ADS  Google Scholar 

  19. S. Wu, U. V. Poulsen, and K. Molmer, Phys. Rev. A: At., Mol., Opt. Phys. 80, 032319 (2009).

    Article  ADS  Google Scholar 

  20. G. Passante, O. Moussa, C. A. Ryan, and R. Laflamme, Phys. Rev. Lett. 103, 250501 (2009).

    Article  ADS  Google Scholar 

  21. B. Dakic, V. Vedral, and C. Brukner, Phys. Rev. Lett. 105, 190502 (2010).

    Article  ADS  Google Scholar 

  22. A. Datta and A. Shaji, Int. J. Quantum Inf. 9, 1787 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  23. G. Passante, O. Moussa, and R. Laflamme, Phys. Rev. A: At., Mol., Opt. Phys. 85, 032325 (2012).

    Article  ADS  Google Scholar 

  24. M. Mehring and J. Mende, Phys. Rev. A: At., Mol., Opt. Phys. 73, 052303 (2006).

    Article  ADS  Google Scholar 

  25. T. Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. 112, 130502 (2014).

    Article  ADS  Google Scholar 

  26. E. I. Kuznetsova and A. I. Zenchuk, Phys. Lett. A 376, 1029 (2012).

    Article  ADS  MATH  Google Scholar 

  27. A. Y. Chernyavskiy, S. I. Doronin, and E. B. Fel’dman, Phys. Scr., T160, 014007 (2014).

    Article  ADS  Google Scholar 

  28. V. E. Zobov, Theor. Math. Phys. 177(1), 1377 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  29. X. Rong, F. Jin, and Z. Wang, Phys. Rev. B: Condens. Matter 88, 054419 (2013).

    Article  ADS  Google Scholar 

  30. F. Reinhard, F. Shi, N. Zhao, F. Rempp, B. Naydenov, J. Meijer, L. T. Hall, L. Hollenberg, J. Du, R.-B. Liu, and J. Wrachtrup, Phys. Rev. Lett. 108, 200402 (2012).

    Article  ADS  Google Scholar 

  31. A. Laraoui, F. Dolde, C. Burk, F. Reinhard, J. Wrachtrup, and C. A. Meriles, Nat. Commun. 4, 1651 (2013).

    Article  ADS  Google Scholar 

  32. T. Fink and H. Bluhm, arXiv:1402.0235.

  33. A. Abragam and M. Goldman, Nuclear Magnetism: Order and Disorder (Clarendon, Oxford, 1982; Mir, Moscow, 1984).

    Google Scholar 

  34. R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Phys. Rev. Lett. 107, 140403 (2011).

    Article  ADS  Google Scholar 

  35. F. Galve, G. L. Giorgi, and R. Zambrini, Europhys. Lett. 96, 40005 (2011).

    Article  ADS  Google Scholar 

  36. D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 92, 067902 (2004).

    Article  ADS  Google Scholar 

  37. S. Boixo, L. Aolita, D. Cavalcanti, K. Modi, M. Piani, and A. Winter, Int. J. Quantum Inf. 9, 1643 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  38. E. B. Fel’dman, E. I. Kuznetsova, and M. A. Yurishchev, J. Phys. A: Math. Theor. 45, 475304 (2012).

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia

    V. E. Zobov

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  1. V. E. Zobov
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Correspondence to V. E. Zobov.

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Original Russian Text © V.E. Zobov, 2014, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 146, No. 5, pp. 933–945.

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Zobov, V.E. Quantum and classical correlations in electron-nuclear spin echo. J. Exp. Theor. Phys. 119, 817–827 (2014). https://doi.org/10.1134/S1063776114110132

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  • DOI: https://doi.org/10.1134/S1063776114110132

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