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

Quantum Gases;Strongly Correlated Electrons;Quantum Physics