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 lattice. We focus our investigation in the experimentally accessible dipolar isotopes of dysprosium ($^{162,164}$Dy), erbium ($^{168}$Er), chromium ($^{52}$Cr), and rubidium ($^{87}$Rb), by considering the binary mixtures ($^{164}$Dy-$^{162}$Dy, $^{168}$Er-$^{164}$Dy, $^{164}$Dy-$^{52}$Cr and $^{164}$Dy-$^{87}$Rb), which are confined in strong pancake-shaped trap and loaded in squared two-dimensional optical lattices, where we vary the polarization angle of 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 to repulsive or attractive the dipole-dipole interactions. For enough higher rotation, of particular interest is the regime when the inter- to intra-species scattering length is larger than one, in which a richer variety of vortex-lattice patterns are predicted, including vortex sheets and two-dimensional rotating droplet formations. The patterns can be controlled by changing the optical lattice parameters, as shown for the symmetric $^{164}$Dy-$^{162}$Dy dipolar mixture. For mixtures with stronger differences in the dipole moments, as $^{164}$Dy-$^{52}$Cr and $^{164}$Dy-$^{87}$Rb, only half quantum vortices and circular ones have been observed, which will depend on the dipole orientations.