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The fermionization regime and entanglement correlations of twodistinguishable harmonically confined fermions interacting via a zero-rangepotential is addressed. We present two alternative representations of theground state that we associate with two different types of one-dimensionalspaces. These spaces, in turn, induce different correlations between particlesand thus require a suitable definition of entanglement. We find that theentanglement of the ground state is strongly conditioned by thoseone-dimensional space features. We also find that in the strongly attractiveregime the relative ground state is a highly localized state leading to maximumentanglement. Our analysis shows that in the strongly repulsive regime theground state changes smoothly from a superposition of Slater-like states to afinite superposition of Slaters, this lack of accessible states yields to Pauliblocking as a strong signature of fermionization. Our results indicate thatentangled states could be obtained in current experiments by reaching thenon-interacting regime from the interacting regime. Entangled states could alsobe obtained when a state is brought from the interacting regime into thestrongly repulsive regime by changing the scattering length near theconfinement-induced resonance. Finally, we show that the first excited stateobtained in the absence of interactions and the third excited fermionized stateare maximally entangled.

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