We explore phases of two-component Rydberg-dressed Bose-Einstein condensates in three spatial dimensions. The competition between the effective ranges of inter- and intra-component soft-core interactions leads to a rich variety of ground states. These include states resembling ionic compounds with face-centered cubic or simple cubic lattice structure. Upon increasing the scattering length, the dimensionality of the symmetry-breaking is lower due to the suppression of large densities, leading to segregated planar or tubular density profiles. We also show that these states are not only stable ground states, but can also emerge dynamically upon time evolution.
Duan et al. (Tue,) studied this question.