Entanglement and fermionization of two distinguishable fermions in a strict and non strict one-dimensional space

TL;DR

This paper investigates how entanglement and fermionization of two distinguishable fermions are affected by different one-dimensional space representations and interaction regimes, revealing conditions for maximum entanglement and signatures of fermionization.

Contribution

It introduces two representations of the ground state based on different 1D spaces and analyzes their impact on entanglement and fermionization in interacting fermions.

Findings

Entanglement is strongly influenced by the space representation.

Maximum entanglement occurs in the strongly attractive regime.

Fermionization manifests as a superposition of Slater states in the strongly repulsive regime.

Abstract

The fermionization regime and entanglement correlations of two distinguishable harmonically confined fermions interacting via a zero-range potential is addressed. We present two alternative representations of the ground state that we associate with two different types of one-dimensional spaces. These spaces, in turn, induce different correlations between particles and thus require a suitable definition of entanglement. We find that the entanglement of the ground state is strongly conditioned by those one-dimensional space features. We also find that in the strongly attractive regime the relative ground state is a highly localized state leading to maximum entanglement. Our analysis shows that in the strongly repulsive regime the ground state changes smoothly from a superposition of Slater-like states to a finite superposition of Slaters, this lack of accessible states yields to Pauli blocking as a strong signature of fermionization. Our results indicate that entangled states could be obtained in current experiments by reaching the non-interacting regime from the interacting regime. Entangled states could also be obtained when a state is brought from the interacting regime into the strongly repulsive regime by changing the scattering length near the confinement-induced resonance. Finally, we show that the first excited state obtained in the absence of interactions and the third excited fermionized state are maximally entangled.