Testing Bell Inequalities Using Topological Aharonov-Casher and He-Mckellar-Wilkens Phases

H.O. Cildiroglu

Lev Vaidman A

S. Lepoutre, A. Gauguet, G. Trénec +2 more

We report an experimental test of the topological phase predicted by He and McKellar in 1993 and by Wilkens in 1994: this phase, which appears when an electric dipole propagates in a magnetic field, is connected to the Aharonov-Casher effect by electric-magnetic duality. The He-McKellar-Wilkens phase is quite small, at most 27 mrad in our experiment, and this experiment requires the high phase sensitivity of our atom interferometer with spatially separated arms as well as symmetry reversals such as the direction of the electric and magnetic fields. The measured value of the He-McKellar-Wilkens phase differs by 31% from its theoretical value, a difference possibly due to some as yet uncontrolled systematic errors.

Jonathan Gillot, S. Lepoutre, A. Gauguet +2 more

In this Letter, we report a measurement of the He-McKellar-Wilkens (HMW) topological phase by atom interferometry. The experiment is done with our lithium atom interferometer, and in order to suppress the stray effects present in our first experiment, we use optical pumping of the (7)Li atoms in their F=2, m(F)=+2 (or -2) ground state sublevel. In these conditions, the measured phase shift is the sum of the HMW phase and of the Aharonov-Casher phase, which are separated due to their different m(F) dependence. The HMW phase has been measured for different lithium beam velocities and the results are in very good agreement with a phase independent of the atom velocity, as expected for a topological phase.

Mohammad Heshmatpour

Anton Zeilinger