The role of internal degrees of freedom in Aharonov-Bohm-type interference phenomena

We show that the pure Aharonov-Bohm (AB) effect, or its dual (DAB), depends only on the net electric, or magnetic charge of an interfering object, however many internal degrees of freedom that system may have. The reciprocal Aharonov-Casher (AC) and He-McKellar-Wilkens (HMW) effects, on the other hand, involve physical properties—the magnetic and electric polarization of the system—which couple a system’s internal degrees of freedom to its center-of-mass coordinate through the field. For composite systems this illustrates a fundamental difference between the two types of phenomenon, and one which could be important as the number of internal degrees of freedom become large. We show that, for a single internal degree of freedom, the result of this coupling is a transient loss of coherence in the observed interference of the center-of-mass coordinate.

Figure 1

(Color online) Schematic representation of the interference experiment. The center-of-mass of the oscillator exists in a superposition of position states at $t=0$, as shown in Eq. (12). This state is assumed to have a momentum directed along the field line toward the screen where the center-of-mass is measured.