Skip to main content
SpringerLink
Log in

An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation

  • Published:
Journal of Contemporary Physics (Armenian Academy of Sciences) Aims and scope

Abstract

We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bell-shaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than 3 × 10−6 for the final transition probability while at certain time points it might increase up to 10−3. Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, M.H., Ensher, J.R., Matthews, M.R., Wieman, C.E., and Cornell, E.A., Science, 1995, vol. 269, p. 198; Davis, K.B., Mewes, M.-O., Andrews, M.R., van Druten, N.J., Durfee, D.S., Kurn, D.M., and Ketterle, W., Phys. Rev. Lett., 1995, vol. 75, p. 3969; Bradley, C.C., Sackett, C.A., Tollett, J.J., and Hulet, R.G., ibid., 1995, vol. 75, p. 1687.

    Article  ADS  Google Scholar 

  2. Phillips, W.D., Rev. Mod. Phys., 1998, vol. 70, p. 721; Cohen-Tannoudji, C.N., Rev. Mod. Phys., 1998, vol. 70, p. 707; Chu, S., Rev. Mod. Phys., 1998, vol. 70, p. 685.

    Article  ADS  Google Scholar 

  3. Thorsheim, H.R., Weiner, J., and Julienne, P.S., Phys. Rev. Lett., 1987, vol. 58, p. 2420; Napolitano, R., Weiner, J., Williams, C.J., and Julienne, P.S., ibid., 1994, vol. 73, p. 1352.

    Article  ADS  Google Scholar 

  4. Stwalley, W.C., Phys. Rev. Lett., 1976, vol. 37, p. 1628; Tiesinga, E., Verhaar, B.J., and Stoof, H.T.C., Phys. Rev. A, 1993, vol. 47, p. 4114.

    Article  ADS  Google Scholar 

  5. Donley, E.A., Claussen, N.R., Thompson, S.T., and Wieman, C.E., Nature, 2002, vol. 417, p. 529; Durr, S., Volz, T., Marte, A., and Rempe, G., Phys. Rev. Lett., 2004, vol. 92, p. 020406; Xu, K., Mukaiyama, T., Abo-Shaeer, J.R., Chin, J.K., Miller, D.E., and Ketterle, W., ibid., 2003, vol. 91, p. 210402; Herbig, J., Kraemer, T., Mark, M., Weber, T., Chin, C., Ngerl, H.-C., and Grimm, R., Science, 2003, vol. 301, p. 1510.

    Article  ADS  Google Scholar 

  6. Regal, C.A., Ticknor, C., Bohn, J.L., and Jin, D.S., Nature, 2003, vol. 424, p. 47; Strecker, K.E., Partridge, G.B., and Hulet, R.G., Phys. Rev. Lett., 2003, vol. 91, p. 080406; Jochim, S. et al., ibid., 2003, vol. 91, p. 240402; Cubizolles, J. et al., ibid., 2003, vol. 91, p. 240401; Greiner, M., Regal, C.A., and Jin, D.S., Nature, 2003, vol. 426, p. 537.

    Article  ADS  Google Scholar 

  7. Zwierlein, M.W., Stan, C.A., Schunck, C.H., Raupach, S.M.F., Gupta, S., Hadzibabic, Z., and Ketterle, W., Phys. Rev. Lett., 2003, vol. 91, p. 250401; Jochim, S., Bartenstein, M., Altmeyer, A., Hendl, G., Riedl, S., Chin, C., and Hecker Denschlag, J., Science, 2003, vol. 302, p. 2101.

    Article  ADS  Google Scholar 

  8. Ishkhanyan, A., Javanainen, J., and Nakamura, H., J. Phys. A, 2005, vol. 38, p. 3505.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Ishkhanyan, A., Javanainen, J., and Nakamura, H., J. Phys. A, 2006, vol. 39, p. 14887

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Sokhoyan, R., Azizbekyan, H., Leroy, C., and Ishkhanyan, A., e-print arXiv:0909.0625, 2009.

  11. Ishkhanyan, A., Joulakian, B., and Suominen, K.-A., J. Phys. B, 2009, vol. 42, p. 221002.

    Article  ADS  Google Scholar 

  12. Barankov, R.A. and Levitov, L.S., arXiv:cond-mat/0506323v1, 2005.

  13. Altman, E. and Vishwanath, A., Phys. Rev. Lett., 2005, vol. 95, p. 110404.

    Article  ADS  Google Scholar 

  14. Tikhonenkov, I., Pazy, E., Band, Y.B., Fleischhauer, M., and Vardi, A., Phys. Rev. A, 2006, vol. 73, p. 043605.

    Article  ADS  Google Scholar 

  15. Dobrescu, B.E. and Pokrovsky, V.L., Phys. Lett. A, 2006, vol. 350, p. 15.

    Article  Google Scholar 

  16. Altland, A. and Gurarie, V., Phys. Rev. Lett., 2008, vol. 100, p. 063602.

    Article  ADS  Google Scholar 

  17. Altland, A., Gurarie, V., Kriecherbauer, T., and Polkovnikov, A., Phys. Rev. A, 2009, vol. 79, p. 042703.

    Article  ADS  Google Scholar 

  18. Itin, A.P., Vasiliev, A.A., Krishna, G., and Watanabe, S., Physica D, 2007, vol. 232, p. 108.

    Article  MATH  ADS  Google Scholar 

  19. Itin, A.P. and Törmä, P., e-print arXiv:0901.4778, 2009.

  20. Sokhoyan, R., Melikdzhanian, D., Leroy, C., Jauslin, H.-R., and Ishkhanyan, A., e-print arXiv:0910.3061 (submitted to Physica D), 2010.

  21. Landau, L.D., Phys. Z. Sowjetunion, 1932, vol. 2, p. 46; Zener, C., Proc. R. Soc. London, 1932, Ser. A, vol. 137, p. 696.

    MATH  Google Scholar 

  22. Demkov, N. and Kunike, M., Vestn. Leningr. Univ., Fiz., Khim., 1969, vol. 16, p. 39; Suominen, K.-A. and Garraway, B.M., Phys. Rev. A, 1992, vol. 45, p. 374.

    MathSciNet  Google Scholar 

  23. Sokhoyan, R., Azizbekyan, H., Leroy, C., and Ishkhanyan, A., J. Contemp. Phys. (Armenian Ac. Sci.), 2006, vol. 44, p. 272.

    Article  Google Scholar 

  24. Sokhoyan, R., Joulakian, B., and Ishkhanyan, A., J. Contemp. Phys. (Armenian Ac. Sci.), 2006, vol. 41, no. 3, p. 1.

    Google Scholar 

  25. Ishkhanyan, A., Joulakian, B., and Suominen, K.-A., Eur. Phys. J. D, 2008, vol. 48, p. 397.

    Article  ADS  Google Scholar 

  26. Sokhoyan, R., J. Contemp. Phys. (Armenian Ac. Sci.), 2010, vol. 45, p. 51.

    Article  Google Scholar 

  27. Javanainen, J. and Mackie, M., Phys. Rev. A, 1999, vol. 59, p. R3186; Kostrun, M., Mackie, M., Cote, R., and Javanainen, J., Phys. Rev. A, 2000, vol. 62, p. 063616; Mackie, M. and Javanainen, J., Phys. Rev. A, 1999, vol. 60, p. 3174.

    Article  ADS  Google Scholar 

  28. Drummond, P.D., Kheruntsyan, K.V., and He, H., Phys. Rev. Lett., 1998, vol. 81, p. 3055; Heinzen, D.J., Wynar, R., Drummond, P.D., and Kheruntsyan, K.V., Phys. Rev. Lett., 2000, vol. 84, p. 5029.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Physical Research, NAS of Armenia, Ashtarak, Armenia

    H. H. Azizbekyan

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation

    H. H. Azizbekyan

  3. LPMC, Université Paul Verlaine — Metz, Metz, France

    H. H. Azizbekyan

Authors
  1. H. H. Azizbekyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © H.H. Azizbekyan, 2010, published in Izvestiya NAN Armenii, Fizika, 2010, Vol. 45, No. 3, pp. 162–172.

About this article

Cite this article

Azizbekyan, H.H. An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation. J. Contemp. Phys. 45, 104–110 (2010). https://doi.org/10.3103/S1068337210030023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068337210030023

Key words

Search

Navigation