# Nonlinear dynamics of a spin-orbit-coupled Bose-Einstein condensate

## TL;DR

This paper investigates how nonlinear interactions affect the dynamics of a spin-orbit-coupled Bose-Einstein condensate, revealing new loop structures in the dispersion relation and their impact on Landau-Zener tunneling.

## Contribution

It introduces the analysis of nonlinear effects on the dispersion relation and tunneling phenomena in spin-orbit-coupled Bose-Einstein condensates, highlighting the emergence of loop structures.

## Key findings

- Nonlinear dispersion develops loop structures due to interactions.
- Loops facilitate nonlinear Landau-Zener tunneling.
- Zitterbewegung remains unaffected by nonlinearity in certain conditions.

## Abstract

Single-particle dynamics of a spin-orbit-coupled Bose-Einstein condensate has recently been investigated in experiments that explore the physics of Landau-Zener tunneling and of the Zitterbewegung. In this paper, we study the influence of a nonlinearity due to interactions on these dynamics and show that the dispersion relation develops interesting loop strucures. The atoms can move along the nonlinear dispersion curve in the presence of a weak acceleration force and we show that the loops lead to straightforward nonlinear Landau-Zener tunneling. However, we find that for the Zitterbewegung, induced by a sudden quench in the spin-orbit coupling parameters, the nonlinear dispersion is irrelevant.