  We investigate the stability of helical superfluid phase in a spin-orbit
coupled Fermi gas loaded in a bilayer optical lattice. The phase diagram of the
system is constructed in the mean field framework. We investigate the
topological properties of the superfluid phases by a nontrivial application of
the Fermi surface topological invariant to our time-reversal invariant system
with degeneracies on the Fermi surface. We find that there is a first-order
phase boundary in the phase diagram of half filling case and the superfluid
phases are all topological trivial. The superfluid phase is topological
nontrivial when the filling fraction deviates from the half filling. In the
topological nontrivial superfluid phase, a full pairing gap exists in the bulk
and gapless helical Majorana edge states exist at the boundary.
