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We have demonstrated a new cooling method in which a time-varying magnetic field gradient is applied to an ultracold spin mixture [1].  We prepare a two-component cloud of rubidium atoms, either in the superfluid or Mott insulator phase, in a strong field gradient separating the two components with a narrow mixed region between the pure-spin domains.  In the Mott insulator, where tunneling is strongly suppressed, reduction of the magnetic field gradient leads to extremely low effective spin temperatures of less than 50 pK.  Reversal of the magnetic field gradient leads to negative spin temperatures, with an absolute value smaller than 50 pK.

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