The wave–particle duality of electrons was demonstrated in a kind of two-slit interference experiment using an electron microscope equipped with an electron biprism and a position-sensitive electron-counting system. Such an experiment has been regarded as a pure thought experiment that can never be realized. This article reports an experiment that successfully recorded the actual buildup process of the interference pattern with a series of incoming single electrons in the form of a movie.
Evidence for the Aharonov-Bohm effect was obtained with magnetic fields shielded from the electron wave. A toroidal ferromagnet was covered with a superconductor layer to confine the field, and further with a copper layer for complete shielding from the electron wave. The expected relative phase shift was detected with electron holography between two electron beams, one passing through the hole of the toroid, and the other passing outside. The experiment gave direct evidence for flux quantization also. P ACS num bers: 03,65.Bz, 41.80.DdThe Aharonov-Bohm (AB) effect' has recently received much attention as an unusual but important quantum effect. The predicted effect is the production of a relative phase shift between two electron beams enclosing a magnetic flux even if they do not touch the magnetic flux. Such an effect is inconceivable in classical physics and directly demonstrates the gauge principle of electromagnetism.Although the affirmative experimental test was offered4 soon after its prediction, Bocchieri et aI. 5 and Roy questioned the validity of the test, attributing the phase shift to leakage fields. The authors' recent experiment using a toroidal magnet established the existence of the AB effect, under the condition of complete confinement of the magnetic field in the magnet; electron holography confirmed quantitatively the expected relative phase shift between the two beams. Bocchieri, Loinger, and Siragusa still argued that the phase shift could be due to the Lorentz-force effect on the portion of the electron beam going through the magnet. 9The present experiment'0 is designed to provide a crucial test of the AB effect. A tiny toroidal magnet covered entirely with a superconductor layer and further with a copper layer is fabricated. The two layers prevent the incident electron wave from penetrating the magnet. In addition, the magnetic field is confined to the toroidal magnet by the Meissner effect of the covering superconductor.Then the relative phase shift between two electron beams, one passing through a region enclosed by the toroid and the other passing outside the toroid, is measured by means of electron holography.The experimental results detected the predicted relative phase shift, giving conclusive evidence for the AB effect. This experiment also demonstrated the flux quantization. " Tiny toroidal samples were fabricated by use of photolithography.
We feel really honoured to give a talk before active researchers in this frontier field of physics, gauge theory and gravity. Although the member of our group are not familiar with the details of concepts and theoretical approachs in this field, we understand the importance of the Aharonov-Bohm effect in the electromagnetism, i.e. the first example of gauge fields. I) 2)-4) Since the theoretical work by Aharonov and Bohm in 1959, several experiments have been performed to prove this effect and these experiments have been fairly famous also among electron-microscopist.We thought the effect has the sound basis beyond doubt but we noticed also that a few people5)still insisted on its non-existance or doubted the validity of the experiments and that the controversy still continued. 6j' Therefore it seemed worth while to try an experiment in a newly designed form to confirm the effect again. This was our motivation.Before going into our experiment, let us explain briefly about those in the past.The schematic diagram in Fig.l shows the idea of the elaborate experiment by M~llenstedt group. 2} ' The lens and bi-prism are, of cource, electro-magnetic ones in fact. They fabricated a fine solenoid coil whose diameter was unbelievably small, 4.7 pm.Two electron waves from the same source travel around the solenoid and are overlapped coherently to cause interference fringes on the film below. Even if the waves never touch the magnetic flux inside the solenoid, the fringe must be shifted with the change in the phase difference between the waves owing to the Aharonov-Bohm effect when the coil current ~ changes. In order to confirm the fringe shift, they set a slit over the recoreding film and moved the film with changing the coil current i.The result is reproduced in Fig.2. The fringe shift is clearly recorded.'3j-4Lre~ " sl i art Other experiments a "m'l o this one in principle except that ferromagnetic needles were used instead of solenoids.All these experiments were very elaborate ones for the technology of those days but we must admit that they have one defect in common. That is, the lack of experimental verifications that there is no magnetic flux leakage into the electron paths.To improve this points, Kuper7)proposed in 1980 the idea of perfect confinement of magnetic fluxon by a hollow torus of super-conductive material, as shown in Fig.3.
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