Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect

TL;DR

This paper explores the topological aspects of the electrodynamic Aharonov-Bohm effect in spacetime, analyzing various configurations to understand phase differences and proposing experimental amplification methods.

Contribution

It introduces new schemes for analyzing the electrodynamic AB effect's topological nature and suggests experimental setups to observe phase amplification.

Findings

AB phase depends on spacetime topology of fields

Connecting wires influence the phase difference

Multiple turns around the solenoid amplify the phase

Abstract

We consider different schemes for the electrodynamic Aharonov-Bohm (AB) effect introduced in Ref. [Phys. Rev. A $\mathbf{108}$, 062218 (2023)], exploring the phenomenon to enhance the understanding of its topological nature in spacetime. In the treated examples, the electric current in a solenoid varies in time, changing its internal magnetic field and producing an external electric field, while a quantum charged particle is in a superposition state inside two Faraday cages in an interferometer. The Faraday cages cancel the electric field at their interiors, such that the particle is always subjected to null electromagnetic fields. We discuss how the AB phase difference depends on the topology of the electric and magnetic fields in spacetime in the different treated situations. In particular, we discuss interesting results when a conducting wire connects the two Faraday cages, with the AB phase depending on the wire position. We also show an amplification of the AB phase when the wire makes several turns around the solenoid, which could enable an experimental verification of the effect.