PRA: MCTDHB for bosons with spin

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Unlike humans in a society, atoms at nearly zero absolute temperature are indistinguishable;
the exchange of the positions of subject A and B has no effect to the system. However, atoms
may form groups with distinct physical properties, like humans in society have diverse opinions
and interests.
A system of indistinguishable bosonic atoms with two internal degrees of freedom is naturally
divided into two groups. As a whole, the two groups may have “the same interests”, i.e., be in
a coherent, condensed state or “have different interests”, i.e., be in an incoherent, fragmented
state.
Herein, we investigate the state of a system of confined two-component bosons and how their
"social behavior" depends on the spatial separation between the components. We find that
members of our “society” of atoms exhibit coherence for small separations. Beyond a critical
separation of the components, the members of distinct components lose coherence while
maintaining it within the components.