# Vortex Lattice Formation in Dipolar Bose-Einstein Condensates via Rotation of the Polarization

## TL;DR

This paper investigates how rotating the polarization of a dipolar Bose-Einstein condensate induces vortex lattice formation, combining analytical solutions, stability analysis, and numerical simulations to reveal a novel vortex creation mechanism.

## Contribution

It introduces a new method of vortex formation in dipolar BECs through polarization rotation, supported by semi-analytical and numerical analysis.

## Key findings

- Rotation of polarization leads to vortex lattice formation.
- Dynamical instabilities seed vortex creation.
- Vortices relax into a triangular lattice configuration.

## Abstract

The behaviour of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilise linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.