  Ultracold atoms in optical lattice provides a platform to realize the
superfluid (SF) state, a quantum order with paired charge-neutral fermions. In
this paper, we studied SF state in the twodimensional attractive Hubbard model
with pi-flux on each plaquette. The SF state in the pi-flux lattice model
suffers very strong quantum fluctuations and the ground state becomes a
possible quantum phase liquid state. In this phase, there exists the Cooper
pairing together with a finite energy gap for the atoms, but no long range SF
phase coherence exists at zero temperature. In addition, we discussed the
properties of the SF vortices.
