  We have recently tested the topological phase predicted by He and McKellar
and by Wilkens: this phase appears when an electric dipole propagates in a
transverse magnetic field. In the present paper, we first recall the physical
origin of this phase and its relations to the Aharononov-Bohm and
Aharonov-Casher phases. We then explain possible detection schemes and we
briefly describe the lithium atom interferometer we have used for this purpose.
Finally, we analyze in great detail the phase shifts induced by electric and
magnetic fields acting on such an interferometer, taking into account
experimental defects. The experiment and its results are described in a
companion paper.
