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The transition into a strongly-correlated regime of 3 fermions trapped in aone-dimensional harmonic potential is investigated. This interesting, butlittle-studied system, allows us to identify characteristic features of theregime, some of which are also present in strongly-correlated materialsrelevant to the industry. Furthermore, our findings describe the behavior ofelectrons in quantum dots, ions in Paul traps, and even fermionic atoms inone-dimensional optical lattices. Near the ground state, all these platformscan be described as fermions trapped in a harmonic potential. The correlationregime can be controlled by varying the natural frequency of the trappingpotential, and to probe it, we propose to use twisted light. We identify 4signatures of strong correlation in the one-dimensional 3-fermion trap, whichare likely to be present for any number N of trapped fermions: i) the groundstate density is strongly localized with N maximally separated peaks (WignerCrystal) ii) the symmetric and antisymmetric ground state wavefunctions becomedegenerate (bosonization) iii) the von Neumann entropy grows, iv) the energyspectrum is fully characterized by N normal modes or less.

Characteristic features of the strongly-correlated regime: Lessons from a 3-fermion one-dimensional harmonic trap