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Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments

  • S. A. Gerasev
  • A. V. Fedorova
  • E. B. Fel’dman
  • E. I. Kuznetsova
Article

Abstract

Quantum correlations are investigated theoretically in a two-spin system with the dipole–dipole interactions in the NMR multiple-pulse spin-locking experiments. We consider two schemes of the multiple-pulse spin-locking. The first scheme consists of \(\pi /2\)-pulses only and the delays between the pulses can differ. The second scheme contains \(\varphi \)-pulses (\(0<\varphi <\pi \)) and has equal delays between them. We calculate entanglement for both schemes for an initial separable state. We show that entanglement is absent for the first scheme at equal delays between \(\pi /2\)-pulses at arbitrary temperatures. Entanglement emerges after several periods of the pulse sequence in the second scheme at \(\varphi =\pi /4\) at milliKelvin temperatures. The necessary number of the periods increases with increasing temperature. We demonstrate the dependence of entanglement on the number of the periods of the multiple-pulse sequence. Quantum discord is obtained for the first scheme of the multiple-pulse spin-locking experiment at different temperatures.

Keywords

Quantum correlations Entanglement Quantum discord Multiple-pulse spin locking Floquet Hamiltonian 

Notes

Acknowledgements

The work is supported by Russian Foundation of Basic Research (Grant No. 16-03-00056) and the Program of the Presidium of the Russian Academy of Sciences No. 5 “Electron spin resonance, spin-dependent electron effects and spin technologies”.

References

  1. 1.
    Haeberlen, U.: Multiple pulse techniques in solid state NMR. Magn. Res. Rev. 10, 81 (1985)Google Scholar
  2. 2.
    Ostroff, E.D., Waugh, J.S.: Multiple spin echoes and spin locking in solids. Phys. Rev. Lett. 16, 1097 (1966)ADSCrossRefGoogle Scholar
  3. 3.
    Mansfield, P.D., Ware, D.: Nuclear resonance line narrowing in solids by repeated short pulse r. f. irradiation. Phys. Lett. 22, 133 (1966)ADSCrossRefGoogle Scholar
  4. 4.
    Ernst H., Fenzke D., Heink W.: Damping of Multiple Spin Echoes in Solids. First Specialized Collîque AMPERE. Krakow, Institute of Nuclear Physics, 122 (1973)Google Scholar
  5. 5.
    Yerofeev, L.N., Shumm, B.A., Manelis, G.B.: Nuclear magnetization relaxation in a multipulse NMR experiment. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 75(5), 1837 (1978)Google Scholar
  6. 6.
    Ivanov, Y.N., Provotorov, B.N., Feldman, E.B.: Thermodynamic theory of NMR spectral-line narrowing in solids. Zhurnal Experimentalnoi i Theoreticheskoi Fiziki 75(5), 1847 (1978)Google Scholar
  7. 7.
    Kuznetsova, E.I., Fel’dman, E.B., Feldman, D.E.: Magnus expansion paradoxes in the study of equilibrium magnetization and entanglement in multi-pulse spin locking. Physics-Uspekhi 59, 577 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    Fel’dman, E.B., Feldman, D.E., Kuznetsova, E.I.: Floquet Hamiltonian and entanglement in spin systems in periodic magnetic fields. Appl. Magn. Reson. 48, 517 (2017)CrossRefGoogle Scholar
  9. 9.
    Goldman, M.: Spin Temperature and Nuclear Magnetic Resonance in Solids. Chapters 1, 2. Clarendon Press, Oxford (1970)Google Scholar
  10. 10.
    Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)ADSCrossRefGoogle Scholar
  11. 11.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefzbMATHGoogle Scholar
  12. 12.
    Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefzbMATHGoogle Scholar
  13. 13.
    Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34, 6899 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  15. 15.
    Fel’dman, E.B., Kuznetsova, E.I., Yurishchev, M.A.: Quantum correlations in a system of nuclear \(s=1/2\) spins in a strong magnetic field. J. Phys. A Math. Theor. 45, 475304 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Abragam, A., Goldman, M.: Nuclear Megnetism: Order and Disorder. Chapter 8. Clarendon Press, Oxford (1982)Google Scholar
  17. 17.
    Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    Bennet, C.H., DiVincenzo, D.P., Fuchs, C.A.: Quantum nonlocality without entanglement. Phys. Rev A 59, 1070 (1999)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Braunstein, S.L., Caves, C.M., Jozca, R., Linden, N., Popescu, S., Schack, R.: Separability of very noisy mixed states and implication for NMR quantum computing. Phys. Rev. Lett. 83, 1054 (1999)ADSCrossRefGoogle Scholar
  20. 20.
    Meyer, D.A.: Sophisticated quantum search without entanglement. Phys. Rev. Lett. 85, 2014 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    Bera A., Das T., Sadhukhan D., Roy S. S., Sen(De) A., Sen U.: Quantum Discord and its allies: a review of recent progress. Reports on Progress in Physics accepted,  https://doi.org/10.1088/1361-6633/aa872f
  22. 22.
    Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Doronin, S.I., Fel’dman, E.B., Kuznetsova, E.I.: Contributions of different parts of spin-spin interactions to quantum correlations in a spin ring model in an external magnetic field. Quantum Inf. Process. 14, 2929 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Yurishchev, M.A.: NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore. JETP 119, 828 (2014)ADSCrossRefGoogle Scholar
  26. 26.
    Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81, 52107 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    Ciliberti, L., Rossignoli, R., Canosa, N.: Quantum discord in finite XY chains. Phys. Rev. A 82, 042316 (2010)ADSCrossRefzbMATHGoogle Scholar
  28. 28.
    Chernyavskiy A. Y.: Calculation of quantum discord and entanglement measures using the random mutations optimization algorithm. arXiv:1304.3703

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Authors and Affiliations

  1. 1.Faculty of Fundamental Physical-Chemical EngineeringLomonosov Moscow State UniversityMoscowRussia
  2. 2.Institute of Problems of Chemical Physics of Russian Academy of SciencesChernogolovkaRussia

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