  The non-Abelian gauge fields play a key role in achieving novel quantum
phenomena in condensed-matter and high-energy physics. Recently, the synthetic
non-Abelian gauge fields have been created in the neutral degenerate Fermi
gases, and moreover, generate many exotic effects. All the previous predictions
can be well understood by the microscopic Bardeen-Cooper-Schrieffer theory. In
this work, we establish an SU(2) Ginzburg-Landau theory for degenerate Fermi
gases with the synthetic non-Abelian gauge fields. We firstly address a
fundamental problem how the non-Abelian gauge fields, imposing originally on
the Fermi atoms, affect the pairing field with no extra electric charge by a
local gauge-field theory,and then obtain the first and second SU(2)
Ginzburg-Landau equations. Based on these obtained SU(2) Ginzburg-Landau
equations, we find that the superfluid critical temperature of the intra-
(inter-) band pairing increases (decreases) linearly, when increasing the
strength of the synthetic non-Abelian gauge fields. More importantly, we
predict a novel SU(2) non-Abelian Josephson effect, which can be used to design
a new atomic superconducting quantum interference device.
