  We study Wilson loops as a necessary tool for unambiguous identification of
non-Abelian synthetic gauge fields, with attention to certain crucial but often
overlooked features, such as the requirement of at least three distinct loops.
We devise a method to determine the complete Wilson loop matrix from the time
evolved amplitudes of the internal atomic states of laser-coupled ultracold
atoms that does not require lattice confinement. The analysis is done in the
context of a new cyclic model that can realize both Abelian and non-Abelian
structures within a single configuration with continuous variation possible
between U(1) and U(2) gauge groups by varying the detuning of the laser fields.
