  We theoretically investigate a three-dimensional Fermi gas with Rashba
spin-orbit coupling in the presence of both out-of-plane and in-plane Zeeman
fields. We show that, driven by a sufficiently large Zeeman field, either
out-of-plane or in-plane, the superfluid phase of this system exhibits a number
of interesting features, including inhomogeneous Fulde-Ferrell pairing, gapped
or gapless topological order and exotic quasi-particle excitations known as
Weyl fermions that have linear energy dispersions in momentum space (i.e.,
massless Dirac fermions). The topological superfluid phase can have either four
or two topologically protected Weyl nodes. We present the phase diagrams at
both zero and finite temperatures and discuss the possibility of their
observation in an atomic Fermi gas with synthetic spin-orbit coupling. In this
context, topological superfluid phases with an imperfect Rashba spin-orbit
coupling are also studied.
