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It is shown theoretically how to directly obtain the energy distribution of aweakly interacting gas of bosons confined in an optical lattice in thetight-binding limit. This is accomplished by adding a linear potential to asuitably prepared lattice, and allowing the gas to evolve under the influenceof the total potential. After a prescribed time, a spectral transform iseffected where each (highly non-local) energy state is transformed into adistinct site of the lattice, thus allowing the energy distribution to be(non-destructively) imaged in real space. Evolving for twice the time returnsthe atoms to their initial state. The results suggest efficient methods to bothmeasure the temperature in situ, as well as to cool atoms within the lattice:after applying the spectral transform one simply needs to remove atoms from allbut a few lattice sites. Using exact numerical calculations, the effects ofinteractions and errors in the application of the lattice are examined.

Cooling ultracold bosons in optical lattices by spectral transform