Evolution of an ultracold gas in a non-Abelian gauge fields: Finite temperature effect

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.