We apply entropy removal by measurement and feedback to a cold atomic spin ensemble. Using quantum nondemolition probing by Faraday rotation measurement, and feedback by weak optical pumping, we drive the initially random collective spin variable F toward the origin F=0. We use input-output relations and ensemble quantum noise models to describe this quantum control process and identify an optimal two-round control procedure. We observe 12 dB of spin noise reduction, or a factor-of-63 reduction in phase-space volume. The method offers a nonthermal route to generation of exotic entangled states in ultracold gases, including macroscopic singlet states and strongly correlated states of quantum lattice gases.
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