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Physical Review Letters

Quantum Effect of the Aharonov-Bohm Type for Particles with an Electric Dipole Moment

Gianfranco Spavieri

Published May 17, 1999• 57 citations
Publisher

Abstract

In the effects of the Aharonov-Bohm type the topological properties of the phase shift are directly related to those of the linear and angular momentum of the electromagnetic fields. This interpretation leads to the formulation of a nonlocal topological effect for particles possessing an electric dipole moment. The experimental observation of this effect is within reach of atom or molecular interferometry.

DOI
10.1103/physrevlett.82.3932

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In the effects of the Aharonov-Bohm type the topological properties of the phase shift are directly related to those of the linear and angular momentum of the electromagnetic fields. This interpretation leads to the formulation of a nonlocal topological effect for particles possessing an electric dipole moment. The experimental observation of this effect is within reach of atom or molecular interferometry.
It is shown that the vector potential of the Aharonov-Bohm effect is effectively the same as vector potentials of the quantum phases of electric and magnetic dipoles such as the Aharonov-Casher effect, when the Aharonov-Bohm solenoid is a straight cylinder with symmetric cross sections. With a circular cross section, the Aharonov-Bohm vector potential is effectively the same as the Aharonov-Casher vector potential, while with a rectangular cross section, it is effectively the same as the vector potential of the Casella phase. Therefore, we may say that the quantum phases of the dipoles belong to a subclass of the Aharonov-Bohm phase, and they must share the topological origin of the Aharonov-Bohm phase, even though their topological freedom is limited to the particle trajectories. However, the dipole phases have the extra relativistic effect that a magnetic (electric) dipole moving in an electric (magnetic) field feels an additional magnetic (electric) field, in its rest frame. This effect limits further the topological freedom of the dipole phases.
The electric Aharonov-Bohm effect is a special case of the general Ab effect. However, when inserting a gravitational potential in the place of the time dependent potential, a different understanding of the phase shift could be gained. The usual topological phase is replaced by a phase with origin in the red shift of the particle at one of the paths taken relative to the other path. In this case, the change in the geometrical measure is the source of the phase shift, which therefore has a local interpretation along with the non-local topological explanation.