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

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.