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

TL;DR

This paper develops an accurate analytical approximation for the weak coupling Landau-Zener transition in a Bose-Einstein condensate, improving understanding of atom-molecular conversion dynamics.

Contribution

It introduces a variational approach based on an auxiliary linear problem to describe the nonlinear Landau-Zener transition in BECs, with enhanced accuracy over previous models.

Findings

The effective Landau-Zener parameter varies non-monotonically with the input parameter.

The approximation accurately predicts the final molecular transition probability.

The method surpasses previous models in precision by an order of magnitude.

Abstract

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.