Quantum Information Processing

, Volume 13, Issue 2, pp 309–321 | Cite as

Entanglement under equilibrium establishing in spin systems subjected to radiofrequency field

  • Gregory B. FurmanEmail author
  • Victor M. Meerovich
  • Vladimir L. Sokolovsky


We study the entanglement evolution in a dipolar-coupled spin system irradiated by a radiofrequency (RF) field in quasi-equilibrium state characterized by a two-temperature density matrix. Process of the establishment of equilibrium is in the equalization of these temperatures. The method of the nonequilibrium statistical operator in a rotating frame is used to describe the evolution of the spin system. It is shown that the equilibrium establishment has nonexponential character, and the time needed for this establishment depends strongly on the RF field strength. Particularly, the weak RF irradiation increases the lifetime of entanglement. Temporal and temperature dependencies of the concurrence of spin pairs are obtained and discussed. It is shown that application of RF field increases the time of the equilibrium establishment (up to order of 1,000 times) and lifetime of the existence of entangled states (up to order of 1,000 times). Thus, with the help of RF irradiation, we can govern the relaxation process and control entanglement in the system. The obtained results can be used for analysis of more complex spin systems because dipole–dipole interaction decreases proportionally to inverse third power of the distance between the spins, and influence of far way spins can be negligible.


Nuclear magnetic resonance Rotating frame Quasi-equilibrium state Entanglement 


  1. 1.
    Benenti, G., Casati, G., Strini, G.: Principles of Quantum Computation and Information, vol. I and II. World Scientific, Singapore (2007)CrossRefzbMATHGoogle Scholar
  2. 2.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008)MathSciNetCrossRefADSzbMATHGoogle Scholar
  3. 3.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 885–942 (2009)MathSciNetCrossRefADSGoogle Scholar
  4. 4.
    Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: Quantum discord and other measures of quantum correlation. Rev. Mod. Phys. 84, 1655–1707 (2012)CrossRefADSGoogle Scholar
  5. 5.
    Amico, L., Osterloh, A.: Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime. J. Phys. A 37, 291–302 (2004)MathSciNetCrossRefADSzbMATHGoogle Scholar
  6. 6.
    Doronin, S.I., Fel’dman, E.B., Kucherov, M.M., Pyrkov, A.N.: Entanglement of systems of dipolar coupled nuclear spins at the adiabatic demagnetization. J. Phys.: Condens. Matter 21, 025601 (5 pp.) (2009)Google Scholar
  7. 7.
    Furman, G.B., Meerovich, V.M., Sokolovsky, V.L.: Entanglement of dipolar coupling spins. Quantum Inf. Process. 10, 307–315 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Furman, G.B., Meerovich, V.M., Sokolovsky, V.L.: Entanglement in dipolar coupling spin system in equilibrium state. Quantum Inf. Process. 11, 1603–1617 (2012)MathSciNetCrossRefADSzbMATHGoogle Scholar
  9. 9.
    Furman, G.B., Meerovich, V.M., Sokolovsky, V.L.: Adiabatic demagnetization and generation of entanglement in spin systems. Phys. Lett. A 376, 925–929 (2012)CrossRefADSGoogle Scholar
  10. 10.
    Galve, F., Pachon, L.A., Zueco, D.: Bringing entanglement to the high temperature limit. Phys. Rev. Lett. 105, 180501 (4 pp.) (2010)Google Scholar
  11. 11.
    Vedral, V.: Quantum physics: hot entanglement. Nature 468, 769–770 (2010)CrossRefADSGoogle Scholar
  12. 12.
    Furman, G.B., Meerovich, V.M., Sokolovsky, V.L.: Fading entanglement near an equilibrium state. Phys. Rev. A 86(3), 032336 (6 pp.) (2012)Google Scholar
  13. 13.
    Atsarkin, V.A., Rodak, M.I.: Temperature of spin-spin interactions in electron spin resonance. Usp. Fiz. Nauk 107, 3 (1972) (Engl. Trans. Sov. Phys.-Usp. 15, 251–265 (1972) )Google Scholar
  14. 14.
    Goldman, M.: Spin Temperature and Nuclear Magnetic Resonance in Solids. Oxford University, New York (1970)Google Scholar
  15. 15.
    Amico, L., Osterloh, A., Plastina, F., Fazio, R., Palma, G.M.: Dynamics of entanglement in one-dimensional spin systems. Phys. Rev. A 69, 022304 (24 pp.) (2004)Google Scholar
  16. 16.
    Subrahmanyam, V.: Entanglement dynamics and quantum-state transport in spin chains. Phys. Rev. A 69, 034304 (4 pp.) (2004)Google Scholar
  17. 17.
    Buric, N.: Influence of the thermal environment on entanglement dynamics in small rings of qubits. Phys. Rev. A 77, 012321 (10 pp.) (2008)Google Scholar
  18. 18.
    Furman, G.B., Meerovich, V.M., Sokolovsky, V.L. : Dynamics of entanglement in a one-dimensional Ising chain. Phys. Rev. A, 77, 062330 (6 pp.) (2008)Google Scholar
  19. 19.
    Furman, G.B., Meerovich, V.M., Sokolovsky, V.L.: Nuclear polarization and entanglement in spin systems. Quantum Inf. Process. 8, 283–291 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Fel’dman, E.B., Pyrkov, A.N.: Evolution of spin entanglement and entanglement witness in multiple quantum NMR experiments. JETP Lett. 88, 454–457 (2008)CrossRefGoogle Scholar
  21. 21.
    Redfield, A.G.: Nuclear magnetic resonance saturation and rotary saturation in solids. Phys. Rev. 98, 1787–1809 (1955)CrossRefADSGoogle Scholar
  22. 22.
    Provotorov, B.N.: Magnetic resonance saturation in crystal. Sov. Phys. JETP 14, 1126–1131 (1962)MathSciNetGoogle Scholar
  23. 23.
    Jeener, J., Eisendrath, H., van Steenwinkel, R.: Thermodynamics of spin systems in solids. Phys. Rev. A 133, A478–A490 (1964)CrossRefADSGoogle Scholar
  24. 24.
    Abragam, A., Goldman, M.: Nuclear Magnetism: Order and Disorder. Clarendon Press, Oxford (1982)Google Scholar
  25. 25.
    Callaghan, P.T., Trotter, C.M., Jolley, K.W.: A pulsed field gradient system for a Fourier transform spectrometer. J. Magn. Reson. 37, 247–259 (1980)ADSGoogle Scholar
  26. 26.
    Abragam, A.: The Principles of Nuclear Magnetism. Clarendon Press, Oxford (1961)Google Scholar
  27. 27.
    Anderson, A.G., Hartman, S.R.: Nuclear magnetic resonance in the demagnetized state. Phys. Rev. 128, 2023–2041 (1962)CrossRefADSzbMATHGoogle Scholar
  28. 28.
    Jeener, J., Bois, R., Du, Broekaert, P.: “Zeeman” and “dipolar” spin temperatures during a strong rf irradiation. Phys. Rev. 135, A1959–A1961 (1965)CrossRefGoogle Scholar
  29. 29.
    Franz, J.R., Slichter, C.P.: Studies of perturbation theory and spin temperature by rotary saturation of spins. Phys. Rev. 148, 287–298 (1966)CrossRefADSGoogle Scholar
  30. 30.
    Kunitomo, M., Hashi, T.: Adiabatic demagnetization in the doubly rotating frame. Phys. Lett. 34A, 157–158 (1971)CrossRefADSGoogle Scholar
  31. 31.
    Zubarev, D.N.: Nonequilibrium Statistical Thermodynamics. Consultants Bureau, New York (1974)Google Scholar
  32. 32.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits phys. Rev. Lett. 80, 2245–2258 (1998)CrossRefADSGoogle Scholar
  33. 33.
    Cho, G., Yesinowski, J.P.: \(^{1}\text{ H }\) and \(^{19}\text{ F }\) multiple-quantum NMR dynamics in quasi-one-dimensional spin clusters in apatites. J. Phys. Chem. 100, 15716–15725 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Gregory B. Furman
    • 1
    Email author
  • Victor M. Meerovich
    • 1
  • Vladimir L. Sokolovsky
    • 1
  1. 1.Physics DepartmentBen Gurion University of the NegevBeer ShevaIsrael

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