  Unitary control of qudits can improve the collective spin squeezing of an
atomic ensemble. Preparing the atoms in a state with large quantum fluctuations
in magnetization strengthens the entangling Faraday interaction. The resulting
increase in interatomic entanglement can be converted into metrologically
useful spin squeezing. Further control can squeeze the internal atomic spin
without compromising entanglement, providing an overall multiplicative factor
in the collective squeezing. We model the effects of optical pumping and study
the tradeoffs between enhanced entanglement and decoherence. For realistic
parameters we see improvements of ~10 dB.
