Blurred path-spin entanglement in Stern-Gerlach apparatus: interplay between magnetic inhomogeneity and Larmor precession

TL;DR

This paper investigates how magnetic field inhomogeneity and Larmor precession affect spin state evolution and entanglement in Stern-Gerlach experiments, revealing non-adiabatic effects that challenge traditional measurement interpretations.

Contribution

It demonstrates that spatial inhomogeneity causes non-adiabatic spin evolution, affecting entanglement and measurement outcomes in Stern-Gerlach setups, with quantitative analysis of conditions for adiabaticity.

Findings

Magnetic inhomogeneity leads to non-adiabatic spin evolution.

Adiabaticity can be restored by adjusting the angle θ.

Path spin entanglement is affected by magnetic field inhomogeneity.

Abstract

We argue that the non-adiabatic evolution of spin states in Stern-Gerlach apparatus can blur the manifestation of path spin entanglement. This fact introduces a contradiction to the usual perception of spin measurement even in a formally ideal situation. Through quantitative calculation, we have pointed out the specific reason behind the breakdown of adiabatic evolution to be the spatial inhomogeneity of applied magnetic field. The angle $\theta$ between the $z$ component of magnetic moment of the particle and applied magnetic field is also a determining factor for the category of evolution of spin states. Adiabaticity always can be restored by choosing a sufficiently small value of $\theta$. Considering azimuthal inhomogeneity, we have examined the nature of path spin entanglement in the context of Stern-Gerlach experiment.