Demkov-Kunike model for cold atom association: weak interaction regime

TL;DR

This paper develops an analytical approximation for molecule formation dynamics in a Bose-Einstein condensate under the Demkov-Kunike model, focusing on the weak interaction regime, with potential applications in cold atom experiments.

Contribution

It introduces a novel approximation method for nonlinear molecule formation dynamics in the Demkov-Kunike model, utilizing a scaled linear solution with variationally determined parameters.

Findings

The approximation accurately describes the weak interaction regime dynamics.

The method simplifies the nonlinear problem to a scaled linear problem.

Analytical expressions for key parameters are derived.

Abstract

We study the nonlinear mean-field dynamics of molecule formation at coherent photo- and magneto-association of an atomic Bose-Einstein condensate for the case when the external field configuration is defined by the quasi-linear level crossing Demkov-Kunike model, characterized by a bell-shaped pulse and finite variation of the detuning. We present a general approach to construct an approximation describing the temporal dynamics of the molecule formation in the weak interaction regime and apply the developed method to the nonlinear Demkov-Kunike problem. The presented approximation, written as a scaled solution to the linear problem associated to the nonlinear one we treat, contains fitting parameters which are determined through a variational procedure. Assuming that the parameters involved in the solution of the linear problem are not modified, we suggest an analytical expression for the scaling parameter.