Light-induced synthetic gauge field in ultracold quantum gases
has received tremendous attention over the past few years. In the case
of a non-Abelian gauge field, the internal pseudo-spin degrees of
freedom and the motional degrees of freedom of the cold atom are
coupled. Such spin-orbit coupling dramatically modifies the
(single-body, few-body, and many-body) properties of the atomic system.
I will briefly review the experimental status of spin-orbit coupled
quantum gases and then focus on recent theoretical works from our group.