From Cooper pairs to Luttinger liquids with bosonic atoms in optical   lattices
  We propose a scheme to observe typical strongly correlated fermionic phenomena with bosonic atoms in optical lattices. For different values of the sign and strength of the scattering lengths it is possible to reach a "superconducting" regime, where the system exhibits atomic pairing, or a Luttinger liquid behavior. We identify the range of parameters where these phenomena appear, illustrate our predictions with numerical calculations, and show how to detect the presence of pairing. 
B. Paredes and J. I. Cirac