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

Abstract

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.