  Motivated by experimental advances on ultracold atoms coupled to a pumped
optical cavity, we propose a scheme for synthesizing and observing the Kondo
insulator in Fermi gases trapped in optical lattices. The synthetic Kondo phase
arises from the screening of localized atoms coupled to mobile ones, which in
our proposal is generated via the pumping laser as well as the cavity. By
designing the atom-cavity coupling, it can engineer a nearest-neighbor-site
Kondo coupling that plays an essential role for supporting topological Kondo
phase. Therefore, the cavity-induced Kondo transition is associated with a
nontrivial topological features, resulting in the coexistence of the
superradiant and topological Kondo state. Our proposal can be realized with
current technique, and thus has potential applications in quantum simulation of
the topological Kondo insulator in ultracold atoms.
