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Quantum dynamics of a three-level trapped ion under a time-dependent interaction with laser beams

  • Rasim DermezEmail author
  • Bekir Deveci
  • Durdu Ö. Güney
Regular Article

Abstract

We solved time-dependent Hamiltonian of a three-level ion interacting with two-laser beams in Λ scheme using a unitary transformation method which transform the Λ scheme to a cascade Ξ scheme for the vibrational phonon transitions. Our analytical results for the probability amplitudes become precise after a certain period of time when the Lamb-Dicke regime is reached. We analyzed the entanglement created in the system.

Keywords

Quantum Information 

References

  1. 1.
    M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)Google Scholar
  2. 2.
    R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    D. Bouwmeester, A. Zeilinger, A. Ekert, The Physics of Quantum Information (Springer, Berlin, 2000)Google Scholar
  4. 4.
    A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935)ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    J.S. Bell, Physics 195, 1 (1964)Google Scholar
  6. 6.
    G. Gour, B.C. Senders, Phys. Rev. Lett. 93, 260501 (2004) ADSCrossRefGoogle Scholar
  7. 7.
    G. Gour, Phys. Rev. A. 71, 012318 (2005) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    R. Dermez, E.Ö. Müstecaplıoğlu, Phys. Scr. 71, 015304 (2009) ADSCrossRefGoogle Scholar
  9. 9.
    R. Dermez, S. Özen, Eur. Phys. J. D 57, 431 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    R. Dermez, S.A. Khalek, J. Russ. Laser Res. 32, 287 (2011)CrossRefGoogle Scholar
  11. 11.
    R. Dermez, S.A. Khalek, K. Kara, B. Deveci, G.N. Gunaydin, J. Russ. Laser Res. 33, 42 (2012)CrossRefGoogle Scholar
  12. 12.
    R. Dermez, S. Özen, Phys. Scr. 85, 055009 (2012) ADSCrossRefGoogle Scholar
  13. 13.
    S. Abdel-Khalek, Phys. Scr. 80, 045302 (2009) ADSCrossRefGoogle Scholar
  14. 14.
    Z.-J. Wang, F. Chen, Chin. Phys. Lett. 24, 1570 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    P. Maunz, Moehring, S. Olmschenk, K.C. Younge, D.N. Matsukevich, C. Monreo, Nature 3, 538 (2007)Google Scholar
  16. 16.
    Mu Qing-Xia, Ma Yang-Hong, L. Zhou, J. Phys. B 40, 3241 (2007) ADSCrossRefGoogle Scholar
  17. 17.
    D.J. Wineland, M. Barrett, J. Britton, J. Chiaverini, B. DeMarco, W.M. Itano, B. Jelenkovici, C. Langer, D. Leibfried, V. Meyer, T. Rosenband, T. Schatz, Philos. Trans. R. Soc. London A 361, 1349 (2003) ADSCrossRefGoogle Scholar
  18. 18.
    R.J. Hughes, D.F.V. James, J.J. Gomez, M.S. Gulley, M.H. Holzscheiter, P.G. Kwiat, S.K. Lamoreau, C.G. Peterson, V.D. Sandberg, M.M. Schauer, C.M. Simmons, C.E. Thorburn, D. Tupa, P.Z. Wang, A.G. White, Fortschr. Phys. 46, 329 (1998)CrossRefGoogle Scholar
  19. 19.
    D. Leibfried, R. Blatt, C. Monroe, D. Wineland, Rev. Mod. Phys. 75, 281 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    J. Criac, P. Zoller, Phys. Rev. Lett. 74, 4091 (1995) ADSCrossRefGoogle Scholar
  21. 21.
    Quantum information with continuous variables of atoms and light, edited by N.J. Cerf, G. Leuchs, E.S. Polzik (Imperial College Press, London, 2007) Google Scholar
  22. 22.
    B.C. Sanders, Appl. Math. Inf. Sci. 3, 117 (2009)MathSciNetGoogle Scholar
  23. 23.
    M. Abdel-Aty, Appl. Phys. B 84, 471 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    D. Leibfried, D.M. Meekhof, B.E. King, C. Monroe, W.M. Itano, D.J. Wineland, J. Mod. Opt. 44, 2485 (1997) ADSGoogle Scholar
  25. 25.
    C. Gerry, P. Knight, Introductory quantum optics (Cambridge University Press, Cambridge, 2005)Google Scholar
  26. 26.
    D.M. Meekhoff, C. Monroe, B.E. King, W.M. Itano, D.J. Wineland, Phys. Rev. Lett. 76, 1796 (1996) ADSCrossRefGoogle Scholar
  27. 27.
    T. Durt, N.J. Cerf, N. Gisin, M. Zukowski, Phys. Rev. A 67, 012311 (2003) ADSCrossRefGoogle Scholar
  28. 28.
    M. Abdel-Aty, A.R. McGurn, Phys. Lett. A 373, 2420 (2009) ADSzbMATHCrossRefGoogle Scholar
  29. 29.
    E.Ö. Müstecaplıoğlu, Phys. Rev. A 68, 023811 (2003) CrossRefGoogle Scholar
  30. 30.
    M. Abdel-Aty, J. Phys. A 38, 8589 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  31. 31.
    M. Abdel-Aty, J. Phys. B 33, 2665 (2000) ADSCrossRefGoogle Scholar
  32. 32.
    D.F.V. James, Appl. Phys. B 66, 181 (1998)ADSCrossRefGoogle Scholar
  33. 33.
    L.F. Wei, Y. Liu, F. Nori, Phys. Rev. A 70, 063801 (2004) ADSCrossRefGoogle Scholar
  34. 34.
    L.F. Wei, Y. Liu, X.L. Lei, Opt. Commun. 208, 131 (2002) ADSCrossRefGoogle Scholar
  35. 35.
    H. Gou, L. Zhao, Phys. Rev. A 73, 053822 (2006) ADSCrossRefGoogle Scholar
  36. 36.
    M. Abdel-Aty, Opt. Commun. 266, 225 (2006) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of PhysicsAfyon Kocatepe UniversityAfyonkarahisarTurkey
  2. 2.Department of Electrical and Computer EngineeringMichigan Technological UniversityHoughtonUSA

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