Adiabatic cooling of fermions in an optical lattice

The entropy-temperature curves are calculated for noninteracting fermions in a three-dimensional optical lattice. These curves facilitate understanding of how adiabatic changes in the lattice depth affect the temperature, and we demonstrate regimes in which the atomic sample can be significantly heated or cooled. When the Fermi energy of the system is near the location of a band gap, the cooling regimes disappear for all temperatures and the system can be heated by only lattice loading. For samples with greater than one fermion per site, we find that lattice loading can lead to a large increase in the degeneracy of the system. We study the scaling properties of the system in the degenerate regimes and assess the effects of nonadiabatic loading.