  The adiabatic theorem, a corollary of the Schr\"odinger equation, manifests
itself in a profoundly different way in non-Hermitian arrangements, resulting
in counterintuitive state transfer schemes that have no counterpart in closed
quantum systems. In particular, the dynamical encirclement of exceptional
points (EPs) in parameter space has been shown to lead to a chiral phase
accumulation, non-adiabatic jumps, and topological mode conversion [1- 8].
Recent theoretical studies, however, have shown that contrary to previously
established demonstrations, this behavior is not strictly a result of winding
around a non-Hermitian degeneracy [9]. Instead, it appears to be mostly
attributed to the non-trivial landscape of the Riemann surfaces, sometimes
because of the presence of an exceptional point in the vicinity [9- 11]. In an
effort to bring this counterintuitive aspect of non-Hermitian systems into
light and confirm this hypothesis, we provide here the first set of experiments
to directly observe the field evolution and chiral state conversion in an
EP-excluding cycle in a slowly varying non- Hermitian system. To do so, a
versatile yet unique fiber-based photonic emulator is realized that utilizes
the polarization degrees of freedom in a quasi-common path single-ring
arrangement. Our observations may open up new avenues for light manipulation
and state conversion, while providing a foundation for understanding the
intricacies of the adiabatic theorem in non-Hermitian systems.
