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

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High Performance Computing in Science and Engineering ’98

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.

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References

  1. F. Haake, Quantum Signatures of Chaos (Springer-Verlag, Berlin 1992).

    Book  Google Scholar 

  2. Quantum Chaos, Eds. G. Casati and B. Chirikov (Cambridge University Press, 1995).

    Google Scholar 

  3. P. W. Anderson, Phys. Rev. 109, 1492 (1958).

    Article  Google Scholar 

  4. F. L. Moore, J. C. Robinson, C. Bharucha, P. E. Williams and M. G. Raizen, Phys. Rev. Lett. 73, 2974 (1994);

    Article  Google Scholar 

  5. theoretical proposal in R. Graham, M. Schlautmann, and P. Zoller, Phys. Rev. A 45, R19 (1992).

    Article  Google Scholar 

  6. M. El Ghafar, P. Törmä, V. Savichev, E. Mayr, A. Zeiler, and W. P. Schleich, Phys. Rev. Lett. 78, 4181 (1997).

    Article  Google Scholar 

  7. W. Paul, Rev. Mod. Phys. 62, 531 (1990).

    Article  Google Scholar 

  8. 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).

    Article  Google Scholar 

  9. 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).

    Article  Google Scholar 

  10. 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. 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).

    Article  Google Scholar 

  13. For a review see for example P. M. Koch and K. A. H. van Leeuwen, Phys. Rep. 255, 289 (1995);

    Article  Google Scholar 

  14. G. Casati, Phys. Rev. A 45, 7670 (1992).

    Article  Google Scholar 

  15. D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano and D. J. Wineland, Phys. Rev. Lett. 76, 1796 (1996);

    Article  Google Scholar 

  16. C. Monroe, D. M. Meekhof, B. E. King and D. J. Wineland, Science 272, 1131 (1996);

    Article  MathSciNet  MATH  Google 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).

    Article  Google Scholar 

  18. G. Birkl, J. A. Yeazell, R. Rückerl, and H. Walther, Europhys. Lett. 27, 197 (1994);

    Article  Google Scholar 

  19. H. Katori, S. Schlipf, and H. Walther, Phys. Rev. Lett. 79, 2221 (1997).

    Article  Google Scholar 

  20. 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. M. Arndt, A. Buchleitner, R. N. Mantegna and H. Walther, Phys. Rev. Lett. 67, 2435 (1991)

    Article  Google Scholar 

  22. F. L. Moore, J. C. Robinson, C. Bharucha, B. Sundaram and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995)

    Article  Google Scholar 

  23. R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, Phys. Rev. A 44, 4521 (1991).

    Article  Google Scholar 

  24. P. Goetsch and R. Graham, Phys. Rev. A 54, 5345 (1996).

    Article  Google Scholar 

  25. A. P. Kazantsev, G. I. Surdutovich and V. P. Yakovlev, Mechanical Action of Light on Atoms (World Scientific, Singapore 1990).

    Book  Google Scholar 

  26. 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. M. D. Feit, J. A. Fleck, JR and A. Steiger, J. of Comput. Phys. 47, 412 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Dum, A. S. Parkins, P. Zoller, and C. W. Gardiner, Phs. Rev. A 46, 4382 (1992)

    Article  Google Scholar 

  30. K. Moelmer, Y. Castin, and J. Dalibard, J. Opt. Soc. Am. B 10, 523 (1993).

    Google Scholar 

  31. J. Javanainen and S. Stenholm, Broad Band Resonant Light Pressure, Appl. Phys. 21, 35 (1980)

    Article  Google Scholar 

  32. H. Carmichael, An Open System Approach to Quantum Optics (Springer—Verlag, Berlin 1991)

    Google Scholar 

  33. G. M. Zaslaysky, Chaos in Dynamic Systems (Harwood Academic Publishers, Chur 1985).

    Google Scholar 

  34. 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. P. J. Bardroff, C. Leichtle, G. Schrade, and W. P. Schleich, Phys. Rev. Lett. 77, 2198 (1996).

    Article  Google Scholar 

  36. S. R. Jefferts, C. Monroe, E. W. Bell, and D. J. Wineland, Phys. Rev. A 51, 3112 (1995).

    Article  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Riedel, K., Törmä, P., Savichev, V., Schleich, W.P. (1999). Dynamical localization in the Paul trap — the influence of the internal structure of the atom. In: Krause, E., Jäger, W. (eds) High Performance Computing in Science and Engineering ’98. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58600-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-58600-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63661-5

  • Online ISBN: 978-3-642-58600-2

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