Dynamical localization in the Paul trap — the influence of the internal structure of the atom

  • Karl Riedel
  • Päivi Törmä
  • Vladimir Savichev
  • Wolfgang P. Schleich
Conference paper

Abstract

We show that quantum localization occurs in the center-of-mass motion of a two-level ion stored in a Paul trap and interacting with a standing laser field. The variable showing localization is identified to be the vibrational quantum number of a reference Floquet oscillator. The quantum localization length is shown to oscillate as a function of the atom-field detuning with a period given by the secular frequency of the trap. Furthermore, we simulate the effect of spontaneous emission on the system and show that in the limit of far detuning the phenomenon of dynamical localization is not destroyed by decoherence.

Keywords

Standing Wave Spontaneous Emission Momentum Distribution Dynamical Localization Localization Length 
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References

  1. 1.
    F. Haake, Quantum Signatures of Chaos (Springer-Verlag, Berlin 1992).CrossRefGoogle Scholar
  2. 2.
    Quantum Chaos, Eds. G. Casati and B. Chirikov (Cambridge University Press, 1995).Google Scholar
  3. 3.
    P. W. Anderson, Phys. Rev. 109, 1492 (1958).CrossRefGoogle Scholar
  4. 4.
    F. L. Moore, J. C. Robinson, C. Bharucha, P. E. Williams and M. G. Raizen, Phys. Rev. Lett. 73, 2974 (1994);CrossRefGoogle Scholar
  5. theoretical proposal in R. Graham, M. Schlautmann, and P. Zoller, Phys. Rev. A 45, R19 (1992).CrossRefGoogle Scholar
  6. 5.
    M. El Ghafar, P. Törmä, V. Savichev, E. Mayr, A. Zeiler, and W. P. Schleich, Phys. Rev. Lett. 78, 4181 (1997).CrossRefGoogle Scholar
  7. 6.
    W. Paul, Rev. Mod. Phys. 62, 531 (1990).CrossRefGoogle Scholar
  8. 7.
    J. C. Robinson, C. Bharucha, F. L. Moore, R. Jahnke, G. A. Georgaki, M. G. Raizen and B. Sundaram, Phys. Rev. Lett. 74, 3963 (1995).CrossRefGoogle Scholar
  9. 8.
    P. J. Bardroff, I. Bialynicki-Birula, D. S. Krähmer, G. Kurizki, E. Mayr, P. Stifter, and W. P. Schleich, Phys. Rev. Lett. 74, 3959 (1995).CrossRefGoogle Scholar
  10. 9.
    In [R. Graham and S. Miyazaki, Phys. Rev. A 53, 2683 (1996)] the problem of atoms in phase modulated standing wave was considered without the adiabatic elimination of the upper state. The emphasis of that paper was, however, on the study of spontaneous emission, not on the effect of the extra quantum degree of freedom as such.Google Scholar
  11. 10.
    R. J. Glauber, Laser manipulation of Atoms and Ions, Proc. Int. School of Physics ‘Enrico Fermi’ Course 118, Eds. E. Arimondo et al. (North Holland, Amsterdam 1992);Google Scholar
  12. see also G. Schrade, P. J. Bardroff, R. J. Glauber, C. Leichtle, V. Yakovlev and W. P. Schleich, Appl. Phys. B 64, 181 (1997).CrossRefGoogle Scholar
  13. 11.
    For a review see for example P. M. Koch and K. A. H. van Leeuwen, Phys. Rep. 255, 289 (1995);CrossRefGoogle Scholar
  14. G. Casati, Phys. Rev. A 45, 7670 (1992).CrossRefGoogle Scholar
  15. 12.
    D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano and D. J. Wineland, Phys. Rev. Lett. 76, 1796 (1996);CrossRefGoogle Scholar
  16. C. Monroe, D. M. Meekhof, B. E. King and D. J. Wineland, Science 272, 1131 (1996);MathSciNetMATHCrossRefGoogle Scholar
  17. D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 77, 4281 (1996).CrossRefGoogle Scholar
  18. 13.
    G. Birkl, J. A. Yeazell, R. Rückerl, and H. Walther, Europhys. Lett. 27, 197 (1994);CrossRefGoogle Scholar
  19. H. Katori, S. Schlipf, and H. Walther, Phys. Rev. Lett. 79, 2221 (1997).CrossRefGoogle Scholar
  20. 14.
    B. Appasamy, Y. Stalgies, J. Eschner, W. Neuhauser, and P. E. Toschek, IQEC’96 Technical Digest (Optical Society of America, Washington DC 1996).Google Scholar
  21. 15.
    M. Arndt, A. Buchleitner, R. N. Mantegna and H. Walther, Phys. Rev. Lett. 67, 2435 (1991)CrossRefGoogle Scholar
  22. F. L. Moore, J. C. Robinson, C. Bharucha, B. Sundaram and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995)CrossRefGoogle Scholar
  23. R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, Phys. Rev. A 44, 4521 (1991).CrossRefGoogle Scholar
  24. 16.
    P. Goetsch and R. Graham, Phys. Rev. A 54, 5345 (1996).CrossRefGoogle Scholar
  25. 17.
    A. P. Kazantsev, G. I. Surdutovich and V. P. Yakovlev, Mechanical Action of Light on Atoms (World Scientific, Singapore 1990).CrossRefGoogle Scholar
  26. 18.
    For more information about the classical dynamics of this system see R. Chacdn and J. I. Cirac, Phys. Rev. A 51, 4900 (1994);Google Scholar
  27. M. El Ghafar, E. Mayr, V. Savichev, P. Törmä, A. Zeiler, and W. P. Schleich, J. Mod. Opt. to appear (1997).Google Scholar
  28. 19.
    M. D. Feit, J. A. Fleck, JR and A. Steiger, J. of Comput. Phys. 47, 412 (1982).MathSciNetMATHCrossRefGoogle Scholar
  29. 20.
    R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, Phs. Rev. A 46, 4382 (1992)CrossRefGoogle Scholar
  30. K. Moelmer, Y. Castin, and J. Dalibard, J. Opt. Soc. Am. B 10, 523 (1993).Google Scholar
  31. 21.
    J. Javanainen and S. Stenholm, Broad Band Resonant Light Pressure, Appl. Phys. 21, 35 (1980)CrossRefGoogle Scholar
  32. 22.
    H. Carmichael, An Open System Approach to Quantum Optics (Springer—Verlag, Berlin 1991)Google Scholar
  33. 23.
    G. M. Zaslaysky, Chaos in Dynamic Systems (Harwood Academic Publishers, Chur 1985).Google Scholar
  34. 24.
    Of course, not any potential is able to cause classical diffusion; for instance for a running wave we found neither classical nor quantum diffusion, because we can define a frame where the ion does not see the potential caused by the running wave.Google Scholar
  35. 25.
    P. J. Bardroff, C. Leichtle, G. Schrade, and W. P. Schleich, Phys. Rev. Lett. 77, 2198 (1996).CrossRefGoogle Scholar
  36. 26.
    S. R. Jefferts, C. Monroe, E. W. Bell, and D. J. Wineland, Phys. Rev. A 51, 3112 (1995).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Karl Riedel
    • 1
  • Päivi Törmä
    • 1
  • Vladimir Savichev
    • 1
  • Wolfgang P. Schleich
    • 1
  1. 1.Abteilung für QuantenphysikUniversität UlmUlmGermany

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