  Recent experiments on fermions in synthetic gauge fields result in systems
with a spin-orbit coupling along one spatial axis, a detuning field, and a
Zeeman field. We show theoretically that the presence of all three results in
interesting and unusual phenomena in such systems in the presence of a contact
singlet attraction between the fermions (described by a scattering length). For
two particles, bound states appear over certain range of the centre of mass
momenta when a critical positive scattering length is attained, with the
deepest bound state appearing at a nonzero centre of mass momentum. For the
centre of mass momenta without a bound state, the gauge field induces a
resonance like feature in the scattering continuum resulting in a large
scattering phase shift. For many particles, we demonstrate that the system, in
a parameter range, shows flow enhanced pairing, i.e., a more robust superfluid
at finite centre of mass momentum. Yet another regime of parameters offers the
opportunity to study strongly interacting normal states of spin-orbit coupled
fermionic systems utilizing the resonance like feature induced by the synthetic
gauge field.
