  We have studied the interference of degenerate quantum gases in a vertical
optical lattice. The coherence of the atoms leads to an interference pattern
when the atoms are released from the lattice. This has been shown for a
Bose-Einstein condensate in early experiments. Here we demonstrate that also
for fermions an interference pattern can be observed provided that the momentum
distribution is smaller then the recoil momentum of the lattice. Special
attention is given to the role of interactions which wash out the interference
pattern for a condensate but do not affect a spin polarized Fermi gas, where
collisions at ultra cold temperatures are forbidden. Comparing the interference
of the two quantum gases we find a clear superiority of fermions for trapped
atom interferometry.
