  We study the stability region of the topological superfluid phase in a
trapped two-dimensional polarized Fermi gas with spin-orbit coupling and across
a BCS-BEC crossover. Due to the competition between polarization, pairing
interaction and spin-orbit coupling, the Fermi gas typically phase separates in
the trap. Employing a mean field approach that guarantees the ground state
solution, we systematically study the structure of the phase separation and
investigate in detail the optimal parameter region for the preparation of the
topologically non-trivial superfluid phase. We then calculate the momentum
space density distribution of the topological superfluid state and demonstrate
that the existence of the phase leaves a unique signature in the trap
integrated momentum space density distribution which can survive the
time-of-flight imaging process.
