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

摘要

In the framework of a basic semiclassical time-dependent nonlinear two-stateproblem, we study the weak coupling limit of the nonlinear Landau-Zenertransition at coherent photo- and magneto-association of an atomicBose-Einstein condensate. Using an exact third-order nonlinear differentialequation for the molecular state probability, we develop a variational approachwhich enables us to construct an accurate analytic approximation describingtime dynamics of the coupled atom-molecular system for the case of weakcoupling. The approximation is written in terms of the solution to an auxiliarylinear Landau-Zener problem with some effective Landau-Zener parameter. Thedependence of this effective parameter on the input Landau-Zener parameter isfound to be unexpected: as the generic Landau-Zener parameter increases, theeffective Landau-Zener parameter first monotonically increases (starting fromzero), reaches its maximal value and then monotonically decreases againreaching zero at some point. The constructed approximation quantitatively welldescribes many characteristics of the time dynamics of the system, inparticular, it provides a highly accurate formula for the final transitionprobability to the molecular state. The present result for the final transitionprobability improves the accuracy of the previous approximation by Ishkhanyanet al. [Phys. Rev. A 69, 043612 (2004); J. Phys. A 38, 3505 (2005)] by order ofmagnitude.