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Journal of International Crisis and Risk Communication Research

Experimental Detection of Forces in an Optical Analog of Aharonov-Bohm Effect

Sergey V. Sukhov, Veerachart Kajorndejnukul, J. Broky, Aristide C. Dogariu

Published Jan 1, 2015• 0 citations
Publisher

Abstract

Wavefront dislocations in scattering create an Aharonov-Bohm setting where nonconservative reaction forces can be detected experimentally. Observing the dynamics of microscopic particles clarifies the role the finite wave-packets on the transfer of wave’s canonical momentum.
DOI
10.1364/cleo_qels.2015.fm2d.8

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The Aharonov–Bohm effect is a fundamental issue in physics. It describes the physically important electromagnetic quantities in quantum mechanics. Its experimental verification constitutes a test of the theory of quantum mechanics itself. The remarkable experiments of Tonomura et al. [“Observation of Aharonov-Bohm effect by electron holography,” Phys. Rev. Lett 48, 1443 (1982) and “Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave,” Phys. Rev. Lett 56, 792 (1986)] are widely considered as the only experimental evidence of the physical existence of the Aharonov–Bohm effect. Here we give the first rigorous proof that the classical ansatz of Aharonov and Bohm of 1959 [“Significance of electromagnetic potentials in the quantum theory,” Phys. Rev. 115, 485 (1959)], that was tested by Tonomura et al., is a good approximation to the exact solution to the Schrödinger equation. This also proves that the electron, that is, represented by the exact solution, is not accelerated, in agreement with the recent experiment of Caprez et al. in 2007 [“Macroscopic test of the Aharonov–Bohm effect,” Phys. Rev. Lett. 99, 210401 (2007)], that shows that the results of the Tonomura et al. experiments can not be explained by the action of a force. Under the assumption that the incoming free electron is a Gaussian wave packet, we estimate the exact solution to the Schrödinger equation for all times. We provide a rigorous, quantitative error bound for the difference in norm between the exact solution and the Aharonov–Bohm Ansatz. Our bound is uniform in time. We also prove that on the Gaussian asymptotic state the scattering operator is given by a constant phase shift, up to a quantitative error bound that we provide. Our results show that for intermediate size electron wave packets, smaller than the ones used in the Tonomura et al. experiments, quantum mechanics predicts the results observed by Tonomura et al. with an error bound smaller than 10−99. It would be quite interesting to perform experiments with electron wave packets of intermediate size. Furthermore, we provide a physical interpretation of our error bound.
A new class of forces, approximately dispersionless forces, were recently predicted as part of a semiclassical description of the Aharonov-Bohm effect. Electron time-of-flight measurements have been performed that test for such forces. Magnetized iron cores used in the previous time-of-flight experiment may affect potential back-action forces and have, therefore, been eliminated. We report that no forces were detected. This finding supports the local and nonlocal, quantum descriptions of the AB effect and rules out local, semiclassical descriptions.
It is shown that the Aharonov-Bohm scattering cross section diverges. This presents a problem since the range of the scattering force (Lorentz force) is finite. The cross section found by Aharonov and Bohm (AB) results whether one takes an incident wave function corresponding to particles moving in the incident direction, as was done by AB, or just takes the incident state to be a plane wave. The mechanism by which a localized force results in an infinite cross section is not clear. This is an apparent contradiction to recent proofs that electrodynamics is a local theory.