Asymmetry and non-dispersivity in the Aharonov-Bohm effect

TL;DR

This paper experimentally investigates the Aharonov-Bohm effect, confirming asymmetry in electron diffraction patterns and providing evidence for a quantum force, while unifying Zeilinger's theorem and Shelankov's prediction under a single theoretical framework.

Contribution

It presents an experiment testing Shelankov's quantum force prediction and offers a theoretical analysis linking it with Zeilinger's theorem, unifying these concepts.

Findings

Asymmetric diffraction pattern observed, confirming Shelankov's prediction.

Experimental evidence suggests the presence of a quantum force.

Theoretical analysis shows both Zeilinger's theorem and Shelankov's result are special cases of a single theorem.

Abstract

Decades ago, Aharonov and Bohm showed that electrons are affected by electromagnetic potentials in the absence of forces due to fields. Zeilinger's theorem describes this absence of classical force in quantum terms as the "dispersionless" nature of the Aharonov-Bohm effect. Shelankov predicted the presence of a quantum "force" for the same Aharonov-Bohm physical system as elucidated by Berry. Here, we report an experiment designed to test Shelankov's prediction and we provide a theoretical analysis that is intended to elucidate the relation between Shelankov's prediction and Zeilinger's theorem. The experiment consists of the Aharonov--Bohm physical system; free electrons pass a magnetized nanorod and far--field electron diffraction is observed. The diffraction pattern is asymmetric confirming one of Shelankov's predictions and giving indirect experimental evidence for the presence of a quantum "force". Our theoretical analysis shows that Zeilinger's theorem and Shelankov's result are both special cases of one theorem.