  To realize non-Abelian s-wave topological superfluid (TS) of cold Fermi
gases, generally a Zeeman magnetic field larger than superfluid pairing gap is
necessary. In this paper we find that using an anisotropic and spin-dependent
optical lattice (ASDOL) to trap gases, a new non-Abelian TS phase appears, in
contrast to an isotropic and spin-independent optical lattice. A characteristic
of this new non-Abelian TS is that Zeeman magnetic field can be smaller than
the superfluid pairing gap. By self-consistently solving pairing gap equation
and considering the competition against normal state and phase separation, this
new phase is also stable. Thus an ASDOL supplies a convenient route to realize
TS. We also investigate edge states and the effects of a harmonic trap
potential.
