Observation of a topological phase by means of a nonplanar Mach-Zehnder interferometer

We report the direct observation of a topological phase, i.e., an Aharonov-Bohm-type phase, as a fringe shift in an optical interferometer, which consisted of a modified Mach-Zehnder interferometer, in which the light traveled along nonplanar paths in its two arms. These arms were arranged symmetrically so as to have nearly equal path lengths, but opposite senses of handedness. The relationship between the phase acquired by a circularly polarized light beam and the solid angle subtended by the circuit of the spin vector of a photon in this beam was found to be a linear one with a slope of unity. The sign of the fringe shift also agreed with theory.