The Effect of Stationary Axisymmetric Spacetimes in Interferometric Visibility

TL;DR

This paper investigates how stationary axisymmetric spacetimes affect the interferometric visibility of a spin-1/2 particle in superposed circular paths, revealing the interplay of proper time and local Wigner rotations on quantum coherence.

Contribution

It introduces a framework for analyzing local Wigner rotations of spin-1/2 particles in stationary axisymmetric spacetimes and explores their impact on quantum interference.

Findings

Proper time differences reduce interferometric visibility.

Local Wigner rotations influence the spin state during superposition.

A general method for studying spin rotations in such spacetimes is proposed.

Abstract

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.