We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase-matched, resulting in exponential enhancement of squeezing. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. A simplified model indicates ~10 dB of squeezing should be achievable with current laboratory parameters.
@article{arxiv.1004.2282,
title = {Strongly Enhanced Spin Squeezing via Quantum Control},
author = {Collin M. Trail and Poul S. Jessen and Ivan H. Deutsch},
journal= {arXiv preprint arXiv:1004.2282},
year = {2013}
}