In order to study the rotating strongly coupled Bose-Einstein condensations (BEC), a holographic model defined in an anti-de Sitter black hole that duals to a coupled two-component condensations in global U(1) symmetry broken phase with intercomponent coupling η and internal coherent coupling ϵ is proposed. By solving the dynamics of the model, we study the process of vortex formation and also the crossover from fractional to integer vortex phases. With changing only η from zero to a finite value, fractional vortex lattices undergo a transition from hexagon to square lattice and finally to vortex sheets. By continuing to turn on ϵ, we find that two fractional vortices in different components constitute dimers, and when η transcends a critical value, multidimer like hexamer or tetramer made up of two and three dimers appears. As ϵ keeps increasing, some dimers rotate to adjust themselves and then constitute the lattice of integer vortices. Under an initial condition similar to a spinor BEC vortices dynamics experiment, the appearance of disordered turbulence is found in the process of fractional vortex generation, which matches the experimental observation. While in the formation process of integer vortices, the appearance of grooves is predicted.
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