# Fingering instabilities and pattern formation in a two-component dipolar Bose-Einstein condensate

## TL;DR

This paper investigates fingering instabilities and pattern formation at the interface of a two-component dipolar Bose-Einstein condensate, revealing spontaneous symmetry breaking and complex pattern emergence due to dipole-dipole interactions.

## Contribution

It demonstrates the spontaneous breaking of rotational symmetry and pattern formation in dipolar BECs, with analytical estimates of domain sizes and effects of various parameters.

## Key findings

- Fingering instability causes symmetry breaking.
- Emergence of frog-shaped and mushroom-shaped patterns.
- Pattern characteristics depend on atom ratio, trap ratio, and polarization tilt.

## Abstract

We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimensional approximation are performed, and the characteristic lengths of the domains are estimated analytically. Patterns resembling those in magnetic classical fluids are modulated when the number ratio of atoms, the trap ratio of the external potential, or tilted polarization with respect to the z direction is varied.