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

TL;DR

This paper investigates the Sagnac effect for spin-1/2 particles by analyzing how local Wigner rotations influence quantum interference, revealing entanglement effects and time delays in superposed paths.

Contribution

It applies the framework of local Wigner rotations to explore the Sagnac effect for spin-1/2 particles, highlighting the role of spin as a quantum clock and its impact on interferometric visibility.

Findings

Spin entanglement affects interferometric visibility.

Proper time differences cause phase shifts in superposed paths.

Wigner rotations provide a geometric understanding of the effect.

Abstract

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)]. 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 to drop, since there is a difference in proper time elapsed along the two trajectories, which is known as the Sagnac time delay.