  We have studied the exotic superfluid phases of degenerated Fermi gases with
spin-orbit coupling in a mixed dimensional system, where the motion of atoms
are free in the x-direction and the tunneling between nearest tubes in the
y-direction is permitted. Using the mean-field method, we obtain the phase
diagrams of the system during the dimensional crossover between quasi one
dimension to quasi two dimension. We find the existence of the topological
state and Majorana edge mode in the weak tunneling case, and a rich phase
diagram including two kinds of nodal superfluid phase and gapped superfluid
phase in the opposite case. Our results show that topological pairing is
favoured in quasi one dimension while nodal pairing state is favoured in quasi
two dimension.
