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 nondemolition measurements, or dissipation in the presence of properly engineered reservoirs. In this Letter we show that two-component Fermi gases at $\sim \mu \mathrm{K}$ temperatures naturally evolve, in the presence of reactive two-body collisions, into states with highly entangled (Dicke-type) spin wave functions. 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 ground state molecules.

Figure 1

The fidelity of the spin density matrix (solid red line, after postselection for a nonvacant well) with respect to the $S_z=0$ Dicke state approaches one (black dotted line) at times long compared to ${\gamma }^{-1}$. The oscillations are due to interwell hopping.

Figure 2

Particle number [$N(t)$, solid red line] and average Dicke state fidelity [$\mathcal{F}(t)$, dashed blue line] for an 8-site Hubbard chain. For $N(t)$, the shaded region is an estimate of the statistical error from sampling of a finite number of trajectories. The black dotted line is the analytic bound in Eq. (3).

Figure 3

(a) An array of $\mathcal{T}$ 1D tubes, each having ${\mathcal{D}}_j$ atoms in a Dicke state. (b) Bloch sphere representation of a Dicke state in a particular tube.