  We propose an experimental scheme to realize non-Abelian dynamical gauge
field for ultracold fermions, which induces a novel pairing mechanism of
topological superfluidity. The dynamical gauge fields arise from nontrivial
interplay effect between the strong Zeeman splitting and Hubbard interaction in
a two-dimensional (2D) optical Raman lattice. The spin-flip transitions are
forbidden by the large Zeeman detuning, but are restored when the Zeeman
splitting is compensated by Hubbard interaction. This scheme allows to generate
a dynamical non-Abelian gauge field that leads to a Dirac type correlated 2D
spin-orbit interaction depending on local state configurations. The topological
superfluid from a novel pairing driven by 2D dynamical gauge fields is reached,
with analytic and numerical results being obtained. Our work may open up a door
to emulate non-Abelian dynamical gauge fields and correlated topological phases
with experimental feasibility.
