Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included

TL;DR

This paper develops an accurate analytic approximation for the dynamics of atom-molecule conversion in a Bose-Einstein condensate, accounting for nonlinear interactions and strong coupling effects in a Landau-Zener transition.

Contribution

It introduces a variational approach to solve a complex nonlinear differential equation, providing a simple analytic description of the coupled atom-molecule system dynamics.

Findings

The approximation accurately describes the time evolution of molecular probability.

It separates the dynamics into molecule formation and oscillation components.

The method accounts for elastic interactions in the strong coupling regime.

Abstract

We study the strong coupling limit of a quadratic-nonlinear Landau-Zener problem for coherent photo- and magneto-association of cold atoms taking into account the atom-atom, atom-molecule, and molecule-molecule elastic scattering. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct a highly accurate and simple analytic approximation describing the time dynamics of the coupled atom-molecule system. We show that the approximation describing time evolution of the molecular state probability can be written as a sum of two distinct terms; the first one, being a solution to a limit first-order nonlinear equation, effectively describes the process of the molecule formation while the second one, being a scaled solution to the linear Landau-Zener problem (but now with negative effective Landau-Zener parameter as long as the strong coupling regime is considered), corresponds to the remaining oscillations which come up when the process of molecule formation is over.