  We study a 1D Fermi gas with attractive short range-interactions in a
disordered potential by the density matrix renormalization group (DMRG)
technique. This setting can be implemented experimentally by using cold atom
techniques. We identify a region of parameters for which disorder enhances the
superfluid state. As disorder is further increased, global superfluidity
eventually breaks down. However this transition occurs before the transition to
the insulator state takes place. This suggests the existence of an intermediate
metallic `pseudogap' phase characterized by strong pairing but no quasi
long-range order.
