Competition between phase coherence and correlation in a mixture of Bose-Einstein condensates

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.