# Decay of the relative phase domain wall into confined vortex pairs: the case of a coherently coupled bosonic mixture

## TL;DR

This paper predicts how a relative phase domain wall in a coherently coupled Bose-Einstein condensate decays through vortex pair formation or snake instability, depending on the Rabi coupling strength, supported by numerical simulations.

## Contribution

It introduces a detailed analysis of decay mechanisms of phase domain walls in coupled BECs, highlighting the role of Rabi coupling strength and providing numerical predictions for experimental setups.

## Key findings

- Small $\Omega$ causes vortex-antivortex pair formation and wall fragmentation.
- Large $\Omega$ leads to snake instability and vortex pair confinement.
- Numerical simulations match experimental sodium gas configurations.

## Abstract

A domain wall of relative phase in a flattened harmonically-trapped Bose-Einstein condensed mixture of two atomic hyperfine states, subject to a stationary Rabi coupling of intensity $\Omega$, is predicted to decay through two different mechanisms. For small values of $\Omega$ the instability has an energetic nature and is associated with the formation of a vortex-antivortex pair of the same atomic hyperfine states, whose motion inside the trap causes the emergence of magnetization, the bending of the domain wall and its consequent fragmentation. For large values of $\Omega$ the domain wall instead undergoes a dynamic snake instability, caused by the negative value of its effective mass and results in the fast fragmentation of the wall into smaller domain walls confining vortex pairs of different atomic species. Numerical predictions are given by solving the time-dependent Gross-Pitaevskii equation in experimentally available configurations of mixtures of sodium atomic gases.