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"Bottom-up" approaches to the many-body physics of fermions have demonstratedrecently precise number and site-resolved preparations with tunability ofinterparticle interactions in single-well, SW, and double-well, DW, nano-scaleconfinements created by manipulating ultracold fermionic atoms with opticaltweezers. These experiments emulate an analogue-simulator mapping onto therequisite microscopic hamiltonian, approaching realization of Feynman's visionof quantum simulators that "will do exactly the same as nature". Here we reporton exact benchmark configuration-interaction computational microscopy solutionsof the hamiltonian, uncovering the spectral evolution, wave-function anatomy,and entanglement properties of the interacting fermions in the entire parameterrange, including crossover from a SW to a DW confinement and a controllableenergy imbalance between the wells. We demonstrate attractive pairing andformation of repulsive, highly-correlated, ultracold Wigner molecules,well-described in the natural orbital representation. The agreement with themeasurements affirms the henceforth gained deep insights into ultracoldmolecules and opens access to the size-dependent evolution of nano-clusteredand condensed-matter phases and ultracold-atoms quantum information.

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Double-well ultracold-fermions computational microscopy: Wave-function  anatomy of attractive-pairing and Wigner-molecule entanglement and natural  orbitals