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

We discuss the strong interaction regime of the nonlinear Landau-Zener problem coming up at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation for the molecular state probability and construct an accurate approximation describing the whole time dynamics of the coupled atom-molecular system. The resultant solution improves the accuracy of the previous approximation by A. Ishkhanyan et al. [J. Phys. A 39, 14887 (2006)]. The obtained results reveal a remarkable observation that in the strong coupling limit the resonance crossing is mostly governed by the nonlinearity while the coherent atom-molecul…