An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation

TL;DR

This paper develops a highly accurate analytical ansatz for modeling ultracold molecule formation dynamics under a nonlinear Demkov-Kunike model, especially in fast sweep and strong interaction regimes, with minimal error.

Contribution

It introduces a novel ansatz that accurately describes nonlinear atom-molecule conversion dynamics in a specific external field configuration, improving understanding of the process.

Findings

Absolute error less than 3*10^-6 in final transition probability

Dynamics consist of nonlinear resonance crossing followed by linear-like oscillations

Effective modeling of ultracold molecule formation in fast sweep regimes

Abstract

We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bell-shaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than 3*10^-6 for the final transition probability while at certain time points it might increase up to 10^-3. Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one.