Line of magnetic monopoles and an extension of the Aharonov-Bohm effect

TL;DR

This paper explores the geometric phase differences in magnetic translation phenomena, extends the Aharonov-Bohm effect to a cylindrical geometry with magnetic monopoles, and proposes an experimental setup to observe these effects.

Contribution

It demonstrates that magnetic translation on a cylinder reproduces the Aharonov-Bohm effect and introduces an experimental extension involving magnetic monopoles in cold atom systems.

Findings

Magnetic translation on a cylinder reproduces the Aharonov-Bohm phase.

The geometric phase differs from the topological phase in certain conditions.

Proposes an experiment to observe the interplay of local and topological phases.

Abstract

In the Landau problem on the two-dimensional plane, magnetic translation of a quantum wave can be induced by an in-plane electric field. The geometric phase accompanying such magnetic translation around a closed path differs from the topological phase of Aharonov and Bohm in two essential aspects: The wave is in direct contact with the magnetic flux and the geometric phase has an opposite sign from the Aharonov-Bohm phase. We show that magnetic translation on the two-dimensional cylinder implemented by the Schr\"odinger time evolution truly leads to the Aharonov-Bohm effect. The magnetic field normal to the cylinder's surface is given by a line of magnetic monopoles which can be simulated in cold atom experiments. We propose an extension of the Aharonov-Bohm experiment which can demonstrate the mutually counteracting effect between the local magnetic translation geometric phase and the topological phase of Aharonov and Bohm.