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A major goal of ultracold atomic physics is quantum simulation of spinHamiltonians in optical lattices. Progress towards this goal requires theattainment of extremely low temperatures. Here we demonstrate a new coolingmethod which consists of applying a time-varying magnetic field gradient to aspin mixture of ultracold atoms. We have used this method to prepare isolatedspin distributions at positive and negative spin temperatures of +/-50picokelvin. The spin system can also be used to cool other degrees of freedom,and we have used this coupling to reduce the temperature of an apparentlyequilibrated sample of rubidium atoms in a Mott insulating state to 350picokelvin. These are the lowest temperatures ever measured in any system.

Spin gradient demagnetization cooling of ultracold atoms