Atomic entanglement generation with reduced decoherence via four-wave mixing

In most proposals for the generation of entanglement in large ensembles of atoms via projective measurements, the interaction with the vacuum is responsible for both the generation of the signal that is detected and the spin depolarization or decoherence. In consequence, one must usually work in a regime where the information acquisition via detection is sufficiently slow (weak measurement regime) such as not to strongly disturb the system. We propose here a four-wave mixing scheme where, owing to the pumping of the atomic system into a dark state, the polarization of the ensemble is not critically affected by spontaneous emission. In the language of spin squeezing, the removal of the limitations imposed by spontaneous emission allows one to work in a strong signal regime where the Heisenberg limit can be reached