Steady-state many-body entanglement of hot reactive fermions

Entanglement is typically created via systematic intervention in the time
evolution of an initially unentangled state, which can be achieved by coherent
control, carefully tailored non-demolition measurements, or dissipation in the
presence of properly engineered reservoirs. In this paper we show that
two-component Fermi gases at ~\mu K temperatures naturally evolve, in the
presence of reactive two-body collisions, into states with highly entangled
(Dicke-type) spin wavefunctions. The entanglement is a steady-state property
that emerges---without any intervention---from uncorrelated initial states, and
could be used to improve the accuracy of spectroscopy in experiments with
fermionic alkaline earth atoms or fermionic groundstate molecules.