  The realization of spin-orbit coupling (SOC) in ultracold atoms has triggered
an intensive exploring of topological superfluids in the degenerate Fermi gases
based on mean-field theory, which has not yet been reported in experiments.
Here, we demonstrate the topological phase transitions in the system via the
numerically exact quantum Monte Carlo method. Without prior assumptions, our
unbiased real-space calculation shows that spin-orbit coupling can stabilize an
unconventional pairing in the weak SOC regime, in which the
Fulde-Ferrell-Larkin-Ovchinnikov pairing coexists with the
Bardeen-Cooper-Schrieffer pairing. Furthermore, we use the jumps in the spin
polarization at the time-reversal invariant momenta to qualify the topological
phase transition, where we find the critical exponent deviated from the
mean-field theory. Our results pave the way for the searching of unconventional
pairing and topological superfluids with degenerate Fermi gases.
