  We consider the simulation of non-abelian gauge potentials in ultracold atom
systems with atom-field interaction in the $\Lambda$ configuration where two
internal states of an atom are coupled to a third common one with a detuning.
We find the simulated non-abelian gauge potentials can have the same structures
as those simulated in the tripod configuration if we parameterize Rabi
frequencies properly, which means we can design spin-orbit coupling simulation
schemes based on those proposed in the tripod configuration. We show the
simulated spin-orbit coupling in the $\Lambda$ configuration can only be of a
form similar to $p_{x}\sigma_{y}$ even when the Rabi frequencies are not much
smaller than the detuning.
