Asymmetry and non-dispersivity in the Aharonov-Bohm effect

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.

16 pages, 5 figures

References in corpus (6)

• Quantum sensing
• Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams
• A macroscopic test of the Aharonov-Bohm effect
• Comment on "Role of Potentials in the Aharonov-Bohm Effect"
• Classical Interaction of a Magnet and a Point Charge: The Shockley-James Paradox
• A Critical Reexamination of the Electrostatic Aharonov-Bohm Effect

Cited by in corpus (7)

• Local description of the Aharonov-Bohm effect with a quantum electromagnetic field
• Electrodynamic Aharonov-Bohm effect
• The Aharonov-Bohm effect in a closed flux line
• Electromagnetic lensing using the Aharonov-Bohm effect
• Evaluating Bohm's quantum force in the scattering process by a classical potential
• Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect
• Topology of the Aharonov-Bohm effect in different reference frames