Unitary cavity spin squeezing by quantum erasure

Deterministic light-induced spin squeezing in an atomic gas is limited by photon shot noise or, equivalently, by atomic state information escaping with the light field mediating the effective atom-atom interaction. We show theoretically that the performance of cavity spin squeezing [M. H. Schleier-Smith, I. D. Leroux and V. Vuletic Phys. Rev. A 81 021804 (2010)] can be substantially improved by erasing the light-atom entanglement, and propose several methods for doing so. Accounting for light scattering into free space, quantum erasure improves the scaling of cavity squeezing from S super(-1/2) to S super(-2/3) where S is the total atomic spin.