Rabi-coupled two-component Bose-Einstein condensates: Classification of the ground states, defects, and energy estimates

We classify the ground states and topological defects of two-component Bose-Einstein condensates under the effect of internal coherent Rabi coupling. We present numerical phase diagrams which show the boundaries between symmetry breaking components and various vortex patterns (triangular, square, bound state between vortices). We estimate the Rabi energy in the Thomas-Fermi limit which allows us to have an analytical description of the point energy leading to the formation of the various vortex patterns.