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We have recently tested the topological phase predicted by He and McKellarand by Wilkens: this phase appears when an electric dipole propagates in atransverse magnetic field. In the present paper, we first recall the physicalorigin of this phase and its relations to the Aharononov-Bohm andAharonov-Casher phases. We then explain possible detection schemes and webriefly describe the lithium atom interferometer we have used for this purpose.Finally, we analyze in great detail the phase shifts induced by electric andmagnetic fields acting on such an interferometer, taking into accountexperimental defects. The experiment and its results are described in acompanion paper.

Test of the He-McKellar-Wilkens topological phase by atom interferometry. Part I: theoretical discussion