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The A to Z of the AB effect

Electrons (blue) passing either side of a current-carrying solenoid shows the Aharonov-Bohm effect in action (Courtesy Physics Today)

By Matin Durrani

The Aharonov-Bohm effect is one of those weird, counter-intuitive consequences of quantum mechanics that makes physics the fascinating subject it is.

Discovered 50 years ago by Yakir Aharonov and the late David Bohm at the University of Bristol in the UK, the AB effect, as it is known to insiders, is being celebrated today at a special conference at Bristol.

In case you weren’t aware, the AB effect describes the fact that an electrically charged particle passing through a region where both the magnetic and electric fields are zero is nevertheless affected by the electromagnetic potential in that region.

It can best be understood by considering a beam of electrons passing through two slits and then around either side of a current-carrying solenoid, as shown by the blue lines in the picture above.

Although there is no magnetic field outside the solenoid, the potential is different on the two sides, which means that the wavefunction of the electrons travelling past one side of the solenoid are phase-shifted by a different amount compared with the electrons travelling past the other.

The AB effect can be verified by allowing the electron beams to interfere: the resulting fringe patterns shift depending on whether the solenoid is on or off.

The conference, which also marks the 25th anniversary of Michael Berry’s discovery of the related “Berry phase”, has attracted a crowd of specialists from around the world, including Aharonov himself.

I went to the conference dinner at the university’s Georgian-period Goldney Hall, where guests were treated to a marvellous menu of roast asparagus with goat’s cheese mousse and Serrano ham crisps, slow-cooked rump of lamb with quince sauce, and confit of raspberries.

Spotted among the guests were Bob Chambers, who confirmed the AB effect experimentally back in 1960, former Brookhaven chairman Michael Hart and independent physicist Julian Barbour, author of The End of Time.

Today’s first lecture session back at the university’s physics department was chaired by Murray Peshkin from Argonne National Laboratory in the US, who introduced Sir Michael by saying “he is a man of few words but many syllables – so listen carefully”.

Berry’s lecture was entitled “Semifluxon degeneracy choreography” and he duly proceded to use a fair few long-syllabled words, including “Gaussian random simulation”, “traceless real symmetric 2×2 matrices” and “rearrangements of nodal domains”.

The talk was a bit over my head, but on such occasions I take comfort in Richard Feynman’s famous phrase that “nobody really understands quantum mechanics”.

The conference ends today.

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  1. John Duffield

    There’s a rather simple way to understand this starting from the right-hand rule. See An electic current travelling vertically up a wire, in the direction of your upraised thumb is associated with a rotational magnetic force in an anticlockwise direction, as per your folded fingers. The electrons exert a “frame dragging” effect on the surrounding space, and the trick to it is to think of a drill bit. If you grip the top of a drill bit in your right fist and push upwards with your left thumb, it turns. For the Aharonov–Bohm effect, you need to extend this analogy to employ one of those flexible drill extensions, and then wrap it into a helical configuration. It still has an effect on the surrounding space, but one which “boosts” or “retards” the electrons travelling on either side rather than imparting a rotational motion or curl.
    See wiki for the moot point that “the profound consequence of Aharonov–Bohm effect was the realisation that the electromagnetic potential offers a more complete description of electromagnetism than the electric and magnetic fields can”. Despite Minkowski’s “wrench” analogy in Space and Time along with Jefimenko’s equations, and despite repeated utterance of the electromagnetic field, many people think of the electric field as something separate to the magnetic field. They aren’t two different things, they’re just two ways of seeing one field in two different ways depending on your motion relative to it.

  2. Thomas Garel

    In Bob Chambers 1960 paper, one can find
    a reference to a 1949 paper (W. Ehrenberg and R. E. Siday, Proc. Phys. Soc. (London) B62, 8 (1949)),where the AB effect is found in a very different “electron optics’ context. See Figure 3 and the disccussion page 21.
    It seems rather strange that the AB effect is not called the ABES effect. Too long for the physics community I guess.

  3. John Duffield

    Interesting, Thomas, thanks. That’s very useful. I’ve just been looking at and I’ll buy this paper. It’s perhaps ironic that the abstract starts with “In view of mis-statements made in the literature, the origin of the refractive index in electron optics is discussed in some detail.. And I said gosh when I turned up this:

  4. pablobham

    Dear all,
    does someone know if the slides of the conference talks are publicly available?

  5. Bob Chambers

    Pity you couldn’t stay for the last session, Matin. It took the form of a splendid verbal joust, lasting over an hour, between the two reigning champions, Yakir Aharonov and Michael Berry, with occasional interjections by others. All very good tempered, very amusing and quite delightful. A good meeting, excellently organised.

  6. The organizers will have slides from the talks online, linked from the Bristol Physics site, in a few days.

  7. John Moran

    I am obviously missing something here, but the description of the effect says that there is no magnetic field outside the solenoid.
    I thought a solenoid produced a field that permeated the space inside and outside its physical confines.
    Please tell me where I’m going wrong.

  8. John Duffield

    John: some articles this are a little misleading, and say things like “The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being zero in the region through which the particle passes”. The interior magnetic field isn’t the cause of the AB effect, the electrons are the cause.
    An electron exhibits an electromagnetic field. It’s isostropic and spherical, and diminishes with distance. If you stack a series of electrons on top of each other, the disposition is now more cylindrical. If you move down past this stack of electrons, you experience a rotation (see rot or curl) that you attribute to a magnetic field, but that’s just how you “see” the electromagnetic field when you’re in relative motion with respect to it. This is why we see braided galactic jets, wherein two electron beams are moving at different velocities.
    It’s also the basis of the right-hand-rule for the current-in-the-wire, see If you move away from the wire, the effect diminishes, but if there’s another wire behind you with the electrons moving in the opposite direction, it doesn’t. Make it a circle of wire, and within the circle the “magnetic field” is fairly uniform. Wrap the wire into a helix like a solenoid, and you’ve got more of the same. There’s a uniform magnetic field inside. Now imagine you can turn the solenoid inside out: the magnetic field is still uniform, but it’s now across the whole of space, so it’s essentially zero. But if you’re just outside the solenoid, you’re near all those electrons moving past you. Their electromagnetic potential doesn’t go away, even though there’s now no measurable rotation as per the current-in-the-wire.

  9. John Duffield

    Probably just an error John. To get back on topic, one of the attendees at ABB 50/25 was Qiu-Hong Hu, author of The nature of the electron, (Physics Essays, Vol. 17, No. 4, 2004) see To my shame I’d forgotten about it, but I think it’s very important. If you look at the ABB50/25 web page at you can see where it says:
    “The Aharonov-Bohm effect and Berry phase describe remarkable aspects of quantum mechanics, which are intrinsic to the nonlocality, geometry and topology of physical systems”.
    This relates to topological quantum field theory, where one sees names like Atiyah and Witten. It can get complicated, but in a nutshell I’d say that to really understand the Aharanov-Bohm effect, one has to understand the electron.

  10. The organizers will have slides from the talks online, linked from the Bristol Physics site, in a few days.


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