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

TL;DR

This paper develops an improved approximation method for the nonlinear Landau-Zener problem in ultracold atom photo- and magneto-association, revealing that nonlinearity dominates resonance crossing while linear dynamics govern post-crossing oscillations.

Contribution

It introduces a variational approach to an exact nonlinear differential equation, enhancing the accuracy of previous models and providing insights into the dominance of nonlinearity during resonance crossing.

Findings

Resonance crossing is mainly governed by nonlinearity in strong coupling.

Post-crossing oscillations are primarily linear in nature.

The new approximation accurately describes the system's evolution across a broad coupling range.

Abstract

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-molecular oscillations coming up soon after the resonance has been crossed are principally of linear nature. This observation is supposed to be general for all the nonlinear quantum systems having the same generic quadratic nonlinearity, due to the basic attributes of the resonance crossing processes in such systems. The constructed approximation turns out to have a larger applicability range (than it was initially expected) covering the whole moderate coupling regime for which the proposed solution accurately describes all the main characteristics of the system's evolution except the amplitude of the coherent atom-molecule oscillation, which is rather overestimated.