# Symmetry breaking of a matter-wave soliton in a double-well potential formed by spatially confined spin-orbit coupling

## TL;DR

This paper investigates how spin-orbit coupling induces symmetry breaking in matter-wave solitons within a double-well potential in spinor Bose-Einstein condensates, revealing new phenomena related to displacement and bimodal symmetry transitions.

## Contribution

It introduces the concept of symmetry breaking in a double-well potential formed by spin-orbit coupling, a novel scenario not previously explored in this context.

## Key findings

- Identification of displacement and bimodal symmetry breaking.
- Control of symmetry transition via interaction strength and spot distance.
- Analysis of symmetry breaking effects in moving systems due to SO coupling.

## Abstract

We consider the symmetry breaking of a matter-wave soliton formed by spinor Bose-Einstein condensates (BECs) illuminated by a two-spot laser beam. This laser beam introduces spin-orbit (SO) coupling in the BECs such that the SO coupling produces an effect similar to a linear doublewell potential (DWP). It is well known that symmetry breaking in a DWP is an important effect and has been discussed in many kinds of systems. However, it has not yet been discussed in a DWP formed by SO coupling. The objective of this work is to study the symmetry breaking of spinor BECs trapped by a DWP formed by SO coupling. We find that two kinds of symmetry breaking, displacement symmetry breaking and bimodal symmetry breaking, can be obtained in this model. The influence of the symmetry transition is systematically discussed by controlling the interaction strength of the BECs and the distance between the center of the two spots. Moreover, because SO coupling violates Galilean invariance, the influence of symmetry breaking in the moving system is also addressed in this paper.