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

Stability of the superfluid state in a disordered 1D ultracold fermionic gas