  We detail the cooling mechanisms of a Fermionic strontium-87 gas in order to
study its evolution under a non-Abelian gauge field. In contrast to our
previous work reported in Ref. [1], we emphasize here on the finite temperature
effect of the gas. In addition, we provide the detail characterization for the
efficiency of atoms loading in the cross-dipole trap, the quantitative
performance of the evaporative cooling, and the characterization of a
degenerate Fermi gas using a Thomas-Fermi distribution.
