# Fingering instabilities and pattern formation in a two-component dipolar Bose-Einstein condensate. (arXiv:1704.04949v2 [cond-mat.quant-gas] UPDATED)

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 analysis in the
two-dimensional approximation are performed, and the characteristic lengths of
the domains are estimated analytically. Patterns in resemblance to those in the
magnetic classical fluids are modulated when the number ratio of atoms, trap
ratio of external potential, or tilted polarization with respect to $z$
direction is varied.