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We discuss the strong interaction regime of the nonlinear Landau-Zenerproblem coming up at coherent photo- and magneto-association of ultracoldatoms. We apply a variational approach to an exact third-order nonlineardifferential equation for the molecular state probability and construct anaccurate approximation describing the whole time dynamics of the coupledatom-molecular system. The resultant solution improves the accuracy of theprevious approximation by A. Ishkhanyan et al. [J. Phys. A 39, 14887 (2006)].The obtained results reveal a remarkable observation that in the strongcoupling limit the resonance crossing is mostly governed by the nonlinearitywhile the coherent atom-molecular oscillations coming up soon after theresonance has been crossed are principally of linear nature. This observationis supposed to be general for all the nonlinear quantum systems having the samegeneric quadratic nonlinearity, due to the basic attributes of the resonancecrossing processes in such systems. The constructed approximation turns out tohave a larger applicability range (than it was initially expected) covering thewhole moderate coupling regime for which the proposed solution accuratelydescribes all the main characteristics of the system's evolution except theamplitude of the coherent atom-molecule oscillation, which is ratheroverestimated.

Strong interaction regime of the nonlinear Landau-Zener problem for photo- and magneto-association of cold atoms