Laser Physics

, Volume 20, Issue 1, pp 291–297 | Cite as

Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate

  • N. Sahakyan
  • H. Azizbekyan
  • H. Ishkhanyan
  • R. Sokhoyan
  • A. IshkhanyanEmail author
Physics of Cold Trapped Atoms


In the framework of a basic semiclassical time-dependent nonlinear two-state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo- and magneto-association of an atomic Bose-Einstein condensate. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom-molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Landau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al. [Phys. Rev. A 69, 043612 (2004); J. Phys. A 38, 3505 (2005)] by order of magnitude.


Laser Phys Laser Physics Molecular State Weak Coupling Limit Auxiliary Parameter 
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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • N. Sahakyan
    • 1
  • H. Azizbekyan
    • 1
    • 2
  • H. Ishkhanyan
    • 2
  • R. Sokhoyan
    • 1
  • A. Ishkhanyan
    • 1
    Email author
  1. 1.Institute for Physical Research NAS of ArmeniaAshtarak-2Armenia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia

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