  In this manuscript, we consider a scenario in which a spin-1/2 quanton goes
through a superposition of co-rotating and counter-rotating geodetic circular
paths, which play the role of the paths of a Mach-Zehnder interferometer in a
stationary and axisymmetric spacetime. Since the spin of the particle plays the
role of a quantum clock, as the quanton moves in a superposed path it gets
entangled with the momentum (or the path), and this will cause the
interferometric visibility (or the internal quantum coherence) to drop, since,
in stationary axisymmetric spacetimes there is a difference in proper time
elapsed along the two trajectories. However, as we show here, the proper time
of each path will couple to the corresponding local Wigner rotation, and the
effect in the spin of the superposed particle will be a combination of both.
Besides, we discuss a general framework to study the local Wigner rotations of
spin-1/2 particles in general stationary axisymmetric spacetimes for circular
orbits.
