Topology of the ground state of two interacting Bose-Einstein condensates

We investigate the spatial patterns of the ground state of two interacting Bose-Einstein condensates. We consider the general case of two different atomic species (with different mass and in different hyperfine states) trapped in a magnetic potential whose eigenaxes can be tilted with respect to the vertical direction, giving rise to a nontrivial gravitational sag. Despite the complicated geometry, we show that within the Thomas-Fermi approximations and upon appropriate coordinate transformations, the equations for the density distributions can be put into a very simple form. Starting from these expressions we give explicit rules to classify the different spatial topologies that can be produced, and we discuss how the behavior of the system is influenced by the interatomic scattering length. We also compare explicit examples with the full numeric Gross-Pitaevskii calculation.