  Two-species hard-core bosons trapped in a three-dimensional isotropic
harmonic potential are studied with the path-integral quantum Monte Carlo
simulation. The double condensates show two distinct structures depending on
how the external potentials are set. Contrary to the mean-field results, we
find that the heavier particles form an outer shell under an identical external
potential whereas the lighter particles form an outer shell under the equal
energy spacing condition. Phase separations in both the spatial and energy
spaces are observed. We provide physical interpretations of these phase
separations and suggest future experiment to confirm these findings.
