Vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates

TL;DR

This paper investigates vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates, revealing how these depend on interaction strengths, polarization angles, and identifying vortex lattice structures.

Contribution

It provides a comprehensive numerical analysis of vortex states and lattice structures in dipolar BECs, including the effect of polarization angle and the identification of a 'magic angle' where critical frequency is unaffected by DDI.

Findings

Critical rotational frequency varies with interaction parameters.

At the magic angle, the critical frequency is nearly independent of DDI strength.

Vortex lattice orientation aligns with dipole polarization direction.

Abstract

Based on the two-dimensional mean-field equations for pancake-shaped dipolar Bose-Einstein condensates in a rotating frame with both attractive and repulsive dipole-dipole interaction (DDI) as well as arbitrary polarization angle, we study the profiles of the single vortex state and show how the critical rotational frequency change with the s-wave contact interaction strengths, DDI strengths and the polarization angles. In addition, we find numerically that at the `magic angle' $\vartheta=\arccos(\sqrt{3}/3)$, the critical rotational frequency is almost independent of the DDI strength. By numerically solving the dipolar GPE at high rotational speed, we identify different patterns of vortex lattices which strongly depend on the polarization direction. As a result, we undergo a study of vortex lattice structures for the whole regime of polarization direction and find evidence that the vortex lattice orientation tends to be aligned with the direction of the dipoles.