Generalized formula for the Landau-Zener transition in interacting Bose-Einstein condensates

TL;DR

This paper derives a highly accurate, generalized Landau-Zener formula for two-level interacting Bose-Einstein condensates, using a variational ansatz and nonlinear differential equations to model the transition probabilities.

Contribution

It introduces a new fifth order polynomial formula for transition probabilities, extending Landau-Zener theory to interacting BECs with high precision.

Findings

Accurate modeling of BEC Landau-Zener transitions.

Development of a fifth order polynomial formula.

Validation of the variational ansatz for all parameters.

Abstract

We present a rigorous analysis of the generalized Landau-Zener problem for the two-level interacting Bose-Einstein condensates. We show that the dynamics of the system is accurately, in detail, described by a two-term variational ansatz that is valid for the whole time domain and is applicable for any set of involved parameters. Applying an exact third order nonlinear differential equation we construct an advanced fifth order polynomial equation for the final transition probability serving as a highly accurate generalized Landau-Zener formula.