  We study the properties of ultracold Fermi gases in a three-dimensional
optical lattice when crossing a Feshbach resonance. By using a zero-temperature
formalism, we show that three-body processes are enhanced in a lattice system
in comparison to the continuum case. This poses one possible explanation for
the short molecule lifetimes found when decreasing the magnetic field across a
Feshbach resonance. Effects of finite temperatures on the molecule formation
rates are also discussed by computing the fraction of double-occupied sites.
Our results show that current experiments are performed at temperatures
considerably higher than expected: lower temperatures are required for
fermionic systems to be used to simulate quantum Hamiltonians. In addition, by
relating the double occupancy of the lattice to the temperature, we provide a
means for thermometry in fermionic lattice systems, previously not accessible
experimentally. The effects of ramping a filled lowest band across a Feshbach
resonance when increasing the magnetic field are also discussed: fermions are
lifted into higher bands due to entanglement of Bloch states, in good agreement
with recent experiments.
