Topological phases reviewed: the Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases.

There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of an electric dipole encircles magnetic charges was realised experimentally, and discuss possible future experimental realisations. © 2014 AIP Publishing LLC.