The Sagnac effect for spin-1/2 particles through local Wigner rotations

In this article, we study the Sagnac effect for spin-1/2 particles through local Wigner rotations, according to the framework developed by H. Terashima and M. Ueda, Phys. Rev. A 69, 032113 (2004). As the particles' spin works as a quantum `clock,' when it moves in a superposition of co-rotating and counter-rotating circular paths in a rotating platform, its spin gets entangled with the momentum due to the local Wigner rotations. Therefore, in contrast with other works in the literature which showed that a rotating space-time (or a rotating frame) causes a shift in the interference pattern, here we show that a rotating space-time also leads to a drop in the interferometric visibility, once there is a difference in the proper time elapsed along the two paths, which is known as the Sagnac time delay.