  We present a systematic theoretical study of the BCS-BEC crossover problem in
three-dimensional atomic Fermi gases at zero temperature with a spherical
spin-orbit coupling which can be generated by a synthetic non-Abelian gauge
field coupled to neutral fermions. Our investigations are based on the path
integral formalism which is a powerful theoretical scheme for the study of the
properties of the bound state, the superfluid ground state, and the collective
excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system
enters the BEC state of a novel type of bound state (referred to as rashbon)
which possesses a non-trivial effective mass. Analytical results and
interesting universal behaviors for various physical quantities at large
spin-orbit coupling are obtained. Our theoretical predictions can be tested in
future experiments of cold Fermi gases with three-dimensional spherical
spin-orbit coupling.
