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A major goal of current research with ultracold atoms in optical lattices is the realization of magnetic ordering.  This requires temperatures on the order of the second order tunneling rate, J2/U where U is the interaction energy and J the tunneling amplitude.  Such temperatures are about ten times less than 1 nk, the lowest temperature reached thus far in optical lattices. Additional cooling methods will be needed to reach this very interesting temperature scale. However, even to assess current methods, new methods of low-temperature thermometry of the Mott insulator are needed.

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