Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave
Akira Tonomura · Nobuyuki Osakabe · Tsuyoshi Matsuda · Takeshi Kawasaki · Junji Endo · Shinichiro Yano · Hiroji Yamada
Summary and citation · read the original at the source · APS default license
In one page
The Aharonov-Bohm effect says that an electron beam which never enters a magnetic field still registers that field, as a shift in the phase of its wave set by the flux it travels around. Akira Tonomura’s group at Hitachi had shown this with tiny ring magnets in 1982, and the standing objection was that some field must still be leaking into the electron’s path. This Letter removes the objection by making leakage physically impossible. The team covered a toroidal ferromagnet with a superconducting layer, which expels magnetic field entirely, and then with a copper layer, so that nothing of the field can reach the electron wave; the relative phase between a beam passing through the hole of the ring and a beam passing outside it was then read out by electron holography. The shift is there. And because a superconductor traps flux only in whole quanta, the measured shift comes out quantised — which is a second result, and a self-check that the shielding worked.
Why it matters hereChapter 10 turns on this experiment: the vector potential is a real influence on matter in a region where the magnetic field is not merely small but shielded away to nothing, and what it controls is phase. Chapter 1 keeps it as the cleanest example on the site of how an argument gets closed — not by debate but by an apparatus in which the leading objection cannot apply, and by a measurement that certifies its own shielding.
What it claims
01Evidence 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.Published abstract, first two sentences
Settled physics02The 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 — one apparatus, two results.Published abstract, final two sentences
Settled physics03The geometry is the argument. A straight solenoid has inevitable leakage fluxes from both ends and an infinite solenoid is experimentally unattainable, but an ideal geometry with no flux leakage can be achieved by the finite system of a toroidal magnetic field — which is why the group moved to toroids and then sealed them inside a superconductor.Tonomura’s own later account of this experiment, Proceedings of the Japan Academy Series B 82, 45 (2006), section ‘Confirmation experiments on the AB effect’
Settled physics04Samples with a range of magnetic flux values were measured, and the relative phase shift was always either zero or half a turn, never anything between. That is exactly what a superconductor enclosing flux requires, because the flux it traps is quantised in units of the Planck constant divided by twice the electron charge: an odd number of trapped vortices gives a half-turn shift, an even number gives none.Tonomura 2006, section ‘Confirmation experiments on the AB effect’, with Figure 2
Settled physics05The quantisation doubles as the control on the whole experiment. Seeing only zero or a half turn confirms that the niobium layer actually became superconducting, that the superconductor completely surrounded the magnetic flux, and that the Meissner effect prevented any flux from leaking out — so the shielding is certified by the same data that shows the effect.Tonomura 2006, section ‘Confirmation experiments on the AB effect’, the paragraph on flux quantization
Settled physics06The conclusion the group draws is unhedged: electron waves passing through the field-free regions inside and outside the toroidal magnet are phase-shifted by half a turn although the waves never touch the magnetic fields, so an electron wave must be physically influenced by the vector potential.Tonomura 2006, closing paragraphs of ‘Confirmation experiments on the AB effect’
Settled physics
The way in
https://doi.org/10.1103/PhysRevLett.56.792WHAT THIS PAGE IS WRITTEN FROM. Physical Review Letters volume 56, issue 8, pages 792 to 795, 1986, by the Hitachi Central Research Laboratory group; the bibliography and the seven-author list were confirmed against the PubMed record, identifier 10033287, and Crossref. The Letter is closed under the APS default licence; OpenAlex and Unpaywall report no open copy and no repository deposit, and on 2026-09-08 the publisher’s own harvest service answered every request for this DOI with ‘not authorized’, so the full Letter could NOT be read for this sheet and no text of it is reproduced here. WHAT WAS READ. First, the complete published abstract, read on 2026-09-08 from the OpenAlex and PubMed records of the Letter, which is the source of the first two claims. Second, and for the experimental detail, Akira Tonomura’s own later account of this same experiment — ‘The Aharonov-Bohm effect and its applications to electron phase microscopy’, Proceedings of the Japan Academy Series B volume 82, pages 45 to 58, 2006, which is open access under a Creative Commons Attribution licence and was read in full from PubMed Central, record PMC4323049; there he introduces this Letter as reference 14 and calls it the last and most conclusive of the series. Locators name whichever of the two each claim is read from. COMPANION PAPER: the group’s full-length treatment is Nobuyuki Osakabe, Tsuyoshi Matsuda, Takeshi Kawasaki, Junji Endo, Akira Tonomura, Shinichiro Yano and Hiroji Yamada, Physical Review A volume 34, pages 815 to 822, 1986.
How to cite it
Akira Tonomura, Nobuyuki Osakabe, Tsuyoshi Matsuda, Takeshi Kawasaki, Junji Endo, Shinichiro Yano, Hiroji Yamada (1986) Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave. doi:10.1103/PhysRevLett.56.792
Where it sits in the curriculum
Scalar waves and the field behind the fieldsThe evidence ladder