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Unitary control of qudits can improve the collective spin squeezing of anatomic ensemble. Preparing the atoms in a state with large quantum fluctuationsin magnetization strengthens the entangling Faraday interaction. The resultingincrease in interatomic entanglement can be converted into metrologicallyuseful spin squeezing. Further control can squeeze the internal atomic spinwithout compromising entanglement, providing an overall multiplicative factorin the collective squeezing. We model the effects of optical pumping and studythe tradeoffs between enhanced entanglement and decoherence. For realisticparameters we see improvements of ~10 dB.

Enhanced squeezing of a collective spin via control of its qudit subsystems