  We describe a measurement-and-feedback technique to deterministically prepare
low-entropy states of atomic spin ensembles. Using quantum non-demolition
measurement and incoherent optical feedback, we drive arbitrary states in the
spin-orientation space toward the origin of the spin space. We observe 12 dB of
spin noise reduction, or a factor of 63 reduction in phase-space volume. We
find optimal feedback conditions and show that multi-stage feedback is
advantageous. An input-output calculation of quantum noise incorporating
realistic quantum noise sources and experimental limitations agrees well with
the observations. The method may have application to generation of exotic
phases of ultracold gases, for example macroscopic singlet states and
valence-bond solids.
