  A microscopic configuration-interaction (CI) methodology is introduced to
enable bottom-up Schroedinger-equation emulation of unconventional
superconductivity in ultracold optical traps. We illustrate the method by
exploring the properties of Lithium-6 atoms in a single square plaquette in the
hole-pairing regime, and by analyzing the entanglement (symmetry-preserving)
and disentanglement physics (via symmetry-breaking, associated with the
separation of charge and spin density waves) of two coupled plaquettes in the
same regime. The single-occupancy RVB states contribute only partially to the
exact many-body solutions, and the CI results map onto a Hubbard Hamiltonian,
but not onto the double-occupancy-excluding t-J one. For the double-plaquette
case, effects brought about by breaking the symmetry between two
weakly-interacting plaquettes, either by distorting, or by tilting and
detuning, one of the plaquettes with respect to the other, as well as spectral
changes caused by increased coupling between the two plaquettes, are explored.
