Studying of experiments related aharonov-bohm type effects

G.N. Afanas'ev

Timothy H. Boyer

Classical electromagnetic lag effects can give rise to quantum interference pattern shifts such as that observed experimentally in the Aharonov-Bohm effect involving electrons passing a solenoid. This paper presents an extensive comparison between interference pattern shifts based upon classical electromagnetic fields, and based upon classical electromagnetic potentials as suggested by Aharonov and Bohm. Stress is placed upon the difference between two types of interference pattern shifts: those involving deflection of the entire interference pattern and those involving a deflection of only the double-slit pattern while leaving the single-slit envelope undisplaced. The first type of shift is produced by a classical deflecting force. The second type of shift can be produced by classical electromagnetic lag effects, and is also the type of shift associated with the Aharonov-Bohm effect. The two types are confused in the literature. A new experiment is proposed which shows the relationship between a classical lag effect, due to electrostatic fields on electrons passing along different paths, and the associated quantum interference pattern shifts. The experiment is analyzed in detail using the WKB approximation in the Schr\"odinger equation and also semiclassical ideas. The classical limit for the situation illustrates the Bohr correspondence principle, showing the relative lag between the electron wave packets becoming a measurable classical lag with a disappearance of the interference pattern as the lag becomes large compared to the wave-packet dimensions. For small shifts, the phase change predicted for the new experiment is identical with the scalar potential effect proposed by Aharonov and Bohm for a slightly different, time-varying experimental arrangement. The theoretical and experimental differences for large phase shifts are noted. The possibility is raised that a new classical electromagnetic lag effect may occur for electrons passing a small solenoid. Using a particular model for energy conservation, the predicted lag effect can be calculated and is associated with a quantum interference pattern shift of the same magnitude as predicted by Aharonov and Bohm based upon the electromagnetic vector potential. Thus the possibility exists that the experiments of Chambers and of M\"ollenstedt and Bayh may not confirm the ideas of Aharonov and Bohm on the vector potential in quantum theory. Several experiments are suggested which allow confirmation that the Aharonov-Bohm effect indeed involves local effects of the classical electromagnetic potential, rather than local electromagnetic fields leading to a new classical lag effect and hence to the observed quantum interference pattern shift.

Vu B Ho, Michael J Morgan

The gravitational Aharonov-Bohm (AB) effect is examined in the weak-field approximation to general relativity. In analogy with the electromagnetic AB effect, we find that a gravitoelectromagnetic 4-vector potential gives rise to interference effects. A matter wave interferometry experiment, based on a modification of the gravity-induced quantum interference experiment of Colella, Overhauser and Werner (COW), is proposed to explicitly test the gravitoelectric version of the AB effect in a uniform gravitational field.

Akira Tonomura

S. A. R. Horsley, M. Babiker, M. R. Singh +1 more

Given that it is now possible to observe the interference of molecules with comparatively numerous internal degrees of freedom, we might wonder what role these extra degrees of freedom play in the traditional double‐slit experiment. Here we seek to understand the effect of these degrees of freedom in an Aharonov‐Bohm type experiment. We find, perhaps unsurprisingly that an ionised object can exhibit the Aharonov‐Bohm effect in a manner which is independent of its internal structure. Meanwhile, the Aharonov‐Bohm type effects involving objects with magnetic, or electric dipole moments (the Aharonov‐Casher and He‐McKellar‐Wilkens effects, respectively) depend explicitly upon the structure. When—due to some specified dynamics of the internal variables—an object’s dipole moment changes during the experiment, we find that the corresponding phase shift depends upon the time average and variance of the internal dynamics. Furthermore, given that the internal dynamics are, to an extent, dependent upon the centre of mass motion there is also a small, transient loss of coherence associated with each internal degree of freedom.

Myron Evans, Jean Pierre Vigier