Vortex patterns in rotating dipolar Bose–Einstein condensate mixtures with squared optical lattices

Vortex-lattice patterns with transitions from regular to other variety vortex shapes are predicted in rotating binary mixtures of dipolar Bose–Einstein condensates loaded in squared optical lattices (OLs). We focus our investigation on the experimentally accessible dipolar isotopes of dysprosium (^162,164Dy), erbium (¹⁶⁸Er), chromium (⁵²Cr), and rubidium (⁸⁷Rb), by considering the binary mixtures (¹⁶⁴Dy-¹⁶²Dy, ¹⁶⁸Er-¹⁶⁴Dy, ¹⁶⁴Dy-⁵²Cr and ¹⁶⁴Dy-⁸⁷Rb), which are confined in strong pancake-shaped traps and loaded in squared two-dimensional (2D) OLs, where we vary the polarization angle of the dipoles, the inter-species contact interactions and the rotation frequency. The ratio between inter- to intra-species contact interaction is used for altering the miscibility properties, with the polarization of the dipolar species used for tuning the dipole–dipole interactions to repulsive or attractive. For enough higher rotation, where the inter- to intra-species scattering length ratio is larger than one, in which a richer variety of vortex-lattice patterns are predicted, including vortex sheets and 2D rotating droplet formations. The patterns can be controlled by changing the OL parameters, as shown for the symmetric ¹⁶⁴Dy-¹⁶²Dy dipolar mixture. For mixtures with stronger differences in the dipole moments, such as ¹⁶⁴Dy-⁵²Cr and ¹⁶⁴Dy-⁸⁷Rb, only half the quantum vortices and circular ones have been observed, which will depend on the dipole orientations. (paper)