  We propose a novel scheme to simulate and observe massless Dirac fermions
with cold atoms in a square optical lattice. A U(1) adiabatic phase is created
by two laser beams for the tunneling of atoms between neighbor lattice sites.
Properly adjusting the tunneling phase, we find that the energy spectrum has
conical points in per Brillouin zone where band crossing occurs. Near these
crossing points the quasiparticles and quasiholes can be considered as massless
Dirac fermions. Furthermore, the anisotropic effects of massless Dirac fermions
are obtained in the present square lattice model. The Dirac fermions as well as
the anisotropic behaviors realizeded in our system can be experimentally
detected with the Bragg spectroscopy technique.
