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Physical Review Letters

Observation of the topological Aharonov-Casher phase shift by neutron interferometry

Alberto Cimmino, G. I. Opat, Andrew G. Klein, Helmut Kaiser, S. A. Werner, M. Arif, R. Clothier

Published Jul 24, 1989• 329 citations
Publisher

Abstract

The phase shift predicted by Aharonov and Casher for a magnetic dipole diffracting around a charged electrode has been observed for the case of thermal neutrons, using a neutron interferometer containing a 30-kV/mm vacuum electrode system. The judicious use of the Earth's gravitational field introduces a spin-independent phase shift which enables unpolarized neutrons to be used. A supplementary magnetic bias field of the correct magnitude allows first-order sensitivity to be achieved; even so, the theoretically predicted phase shift is only 1.50 mrad for the geometry and conditions of the experiment. We observe a phase shift of 2.19\ifmmode\pm\else\textpm\fi{}0.52 mrad.

DOI
10.1103/physrevlett.63.380

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The phase shift predicted by Aharonov and Casher for a magnetic dipole diffracting around a charged electrode has been observed for the case of thermal neutrons, using a neutron interferometer containing a 30-kV/mm vacuum electrode system. The judicious use of the Earth's gravitational field introduces a spin-independent phase shift which enables unpolarized neutrons to be used. A supplementary magnetic bias field of the correct magnitude allows first-order sensitivity to be achieved; even so, the theoretically predicted phase shift is only 1.50 mrad for the geometry and conditions of the experiment. We observe a phase shift of 2.19\ifmmode\pm\else\textpm\fi{}0.52 mrad.
We have measured the phase shift predicted by Aharonov and Casher (AC) for a magnetic dipole diffracting around a charged electrode for the case of thermal neutrons, using a neutron interferometer containing a 30‐kV/mm vacuum electrode system. Tilting the interferometer about the incident beam direction introduces a spin‐independent gravitationally‐induced phase shift which enables unpolarized neutrons to be used. A supplementary magnetic bias field of the correct magnitude allows first‐order sensitivity to the AC phase shift to be achieved. Nevertheless, the theoretically predicted phase shift is only 1.52 mrad for the geometry and conditions of the experiment. We observe a phase shift of 2.11±0.34 mrad. A detailed description of the experiment and its interpretation is given in this paper.
Experiments involving quantum interference of neutron de Broglie waves, having a wavelength A , extending over macroscopic distances of order are described. In particular I discuss interference induced by the Earth's gravitational field and by its rotation (Sagnac effect), the topological phase shifts resulting from the diffraction of the neutron, carrying its magnetic moment , around a charged electrode (Aharonov--Casher effect) and then finally during its passage through a pulsed magnetic field (scalar Aharonov--Bohm effect).
The special and unique techniques of neutron interferometry have been used to observe a number of topological effects. These include the quantum mechanical phase shift of a neutron due to the Earth's rotation (the quantum analog of the Michelson–Gale–Pearson experiment with light), the phase shift of a particle carrying a magnetic moment (a neutron) encircling a line charge (the Aharonov–Casher effect) and the scalar Aharonov–Bohm effect, observed with a pulsed magnetic field solenoid and time-of-flight neutron detection. On the occasion of the 50th anniversary of the Aharonov–Bohm paper, we provide an overview of the neutron interferometry technique and a description of these three historic experiments.
The usual vector Aharonov–Bohm effect involves the quantum interference of electrons encircling a solenoid due to the magnetic vector potential. The analogous Aharonov–Casher effect was predicted for the neutron, which carries a magnetic dipole moment, encircling a line of electric charge . It was first observed by neutron interferometry, as described in this chapter. An analogous effect using neutrons and a pulsed magnetic solenoid in one leg of the interferometer has also been observed. This experiment using both polarized and unpolarized neutrons is described in this chapter. It is the first observation of the scalar Aharonov-Bohm effect. The idea of geometric phases was later shown to be pervasive in physics. These ideas were brought to full fruition in a neutron interferometry experiment in the late 1990s. The connections of this experiment with the helical field experiment of Bitter and Dubbers and the absorption experiment of Hasegawa are also discussed. The confinement-induced phase when neutrons move between narrow plates is another example of a non-local interaction of neutrons.
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 Aharonov-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 the following paper.
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.