  Geometric phases appear ubiquitously in many and diverse areas of physical
sciences, ranging from classical and molecular dynamics to quantum mechanics
and solid-state physics. In the realm of optics, similar phenomena are known to
emerge in the form of a Pancharatnam-Berry phase whenever the polarization
state traces a closed contour on the Poincare sphere. While this class of
geometric phases has been extensively investigated in both free-space and
guided wave systems, the observation of similar effects in photon-tunneling
arrangements has so far remained largely unexplored. Here, for the first time,
we experimentally demonstrate that the tunneling or coupling process in a
twisted multi-core fiber system can display a chiral geometric phase
accumulation-analogous to that of the Aharonov-Bohm effect resulting from the
presence of a nonzero magnetic flux. In our experiments, the tunneling
geometric phase is manifested through the interference of the corresponding
supermodes. In this system, and for specific values of the twist rate, the
tunneling between opposite cores ceases, thus signifying an Aharonov-Bohm
suppression of tunneling. Our work provides the first observation of this
intriguing effect in an optical setting.
