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 (CIR). Finally, we show that the first excited state obtained in the absence of interactions and the third excited fermionized state are maximally entangled.

讨论了通过零范围电势相互作用的两个可区分的谐波受限费米子的费米化过程和缠结关系。我们提出了与两种不同类型的一维空间相关联的基态的两种替代表示。这些空间又在粒子之间引起不同的相关性，因此需要对缠结进行适当的定义。我们发现，基态的纠缠强烈地由那些一维空间特征决定。我们还发现，在极具吸引力的体制中，相对基态是高度局部化的状态，从而导致最大的纠缠。我们的分析表明，在强排斥状态下，基态从类斯拉特状态的叠加到斯拉特的有限叠加平稳地变化，缺乏可访问国家的情况使Pauli封锁成为fermionization的有力标志。我们的结果表明，在当前的实验中，通过从相互作用体系达到非相互作用体系，可以获得纠缠态。当将状态从相互作用状态引入强排斥状态时，可以通过更改限制诱导共振（CIR）附近的散射长度来获得纠缠状态。最后，我们证明了在没有相互作用的情况下获得的第一激发态和第三费米离子化态被最大程度地纠缠了。当将状态从相互作用状态引入强排斥状态时，可以通过更改限制诱导共振（CIR）附近的散射长度来获得纠缠状态。最后，我们证明了在没有相互作用的情况下获得的第一激发态和第三费米离子化态被最大程度地纠缠了。当将状态从相互作用状态引入强排斥状态时，可以通过更改限制诱导共振（CIR）附近的散射长度来获得纠缠状态。最后，我们证明了在没有相互作用的情况下获得的第一激发态和第三费米离子化态被最大程度地纠缠了。