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

• Published in: arXiv.org 2021-08
• Main Authors: Cuestas, Eloisa, Jiménez, Martín D, Majtey, Ana P
• Format: Article
• Language: English
• Subjects: Entangled states; Entanglement; Fermions; Ground state; Resonance scattering
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2108.10389

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.