Quantum Degeneracy and Spin Entanglement in Ideal Quantum Gases

Quantum degeneracy is the central many-body feature of ideal quantum gasesstemming from quantum mechanics. In this work we address its relationship tothe most fundamental form of non-classicality in many-body system, i.e.many-body entanglement. We aim at establishing a quantitative link betweenquantum degeneracy and entanglement in spinful ideal gases, using entanglementwitness criteria based on the variance of the collective spin of the spinensemble. We show that spin-1/2 ideal Bose gases do not possess entanglementwhich can be revealed from such entanglement criteria. On the contrary, idealspin-1/2 Fermi gases exhibit spin entanglement revealed by the collective-spinvariances upon entering quantum degeneracy, due to the formation of highlynon-local spin singlets. We map out the regime of detectable spin entanglementfor Fermi gases in free space as well as in a parabolic trap, and probe therobustness of spin entanglement to thermal effects and spin imbalance. Spinentanglement in degenerate Fermi gases is amenable to experimental observationusing state-of-the-art spin detection techniques in ultracold atoms.