Aharonov-Bohm Effect

Could someone (other than Jim Choate) explain the mechanism behind the
Aharonov-Bohm effect, where a quantum field propagating via two distinct
paths finds its wavefunction phase shifted by the amount of magnetic flux
enclosed, even if it is completely shielded from the magnetic field, and
traverses only regions of space where B=0.

This has apparently been experimentally verified, and is a leading
candidate for reading the state of quantum dots.  

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Eric Cordian wrote:
> 
> Could someone (other than Jim Choate) explain the mechanism behind the
> Aharonov-Bohm effect, where a quantum field propagating via two
> distinct paths finds its wavefunction phase shifted by the amount of magnetic
> flux enclosed, even if it is completely shielded from the magnetic field,
> and traverses only regions of space where B=0.

What do you actually want explaining? Although the magnetic field is
zero along the paths traveled (so that electrons never feel the magnetic
field and the Lorentz force that affects a moving charge in one), the
vector
potential field is not, and is different for the two paths. This causes
the
AB-effect. See, for example G.Baym, 'Lectures on Quantum Mechanics'
(Benjamin, NY, 1969) page 77-79.

> This has apparently been experimentally verified,

Yup, one of the best being N.Osakabe et al, Physics Review A, v34, page
815,
(1986).

> and is a leading candidate for reading the state of quantum dots.

I think you have that the wrong way round - the state of Q. dots is
easy to measure, and so if you put a QD in one arm of an Aharonov-Bohm
interferometer, then measuring the state of the dot allows you know
which path an electron took. If you know that, the wavefunction of
the electron collapses to include just one path, so there is no
interference.
Eyal Buks et al demonstrated this last year - as they increased the
sensitivity of the probe to measure the occupancy of the quantum dot,
the Aharonov-Bohm oscillations in what was classical a separate
system died away.

If you want more details, I'll be happy to explain more. Maybe we should
take it off-list, though, as I seem to have accidently included
references and an informed opinion in my reply, rather than a bigoted
rant.

As for relevance, it is left as an exercise for the reader to work out
why it might be useful to in principle measure fluctuations in a
magnetic
field which is heavily screened, and it's application to cryptography
and
privacy.


Tim

--
Tim Griffiths                   griffith@wis.weizmann.ac.il
Center for Submicron Research   http://tim01.ex.ac.uk
Weizmann Institute of Science   (972)-8-934-2736
Rehovot 76100 Israel

 'I have sat and listened to the arguments of men,
  and I tell you they are shallow movements in space
  tied to reality only by the ego of their minds.' -DF

Tim Griffiths <griffith@wis.weizmann.ac.il> writes:
 
> What do you actually want explaining? Although the magnetic field is
> zero along the paths traveled (so that electrons never feel the
> magnetic field and the Lorentz force that affects a moving charge in
> one), the vector potential field is not, and is different for the two
> paths. This causes the AB-effect. See, for example G.Baym, 'Lectures
> on Quantum Mechanics' (Benjamin, NY, 1969) page 77-79.
 
Why do I find this odd?  Because the electromagnetic field acts
locally, the vector potential is not directly observable and depends
on ones choice of gauge, and wavefunction phase is also not directly
observable.  The integral of the vector potential around the closed
path is of course well-defined, but this is global, not local.
 
So it seems strange, and hints at some sort of "action at a distance"
thing occuring.  The wavefunction is being perturbed according to the
magnetic flux enclosed by a path, even while propagating in a region
distant to the flux which contains no electromagnetic field at all.
 
> As for relevance, it is left as an exercise for the reader to work out
> why it might be useful to in principle measure fluctuations in a
> magnetic field which is heavily screened, and it's application to
> cryptography and privacy.
 
It still seems counterintuitive to suggest that I can make a tour
around a magnetic field an arbitrary distance away, and get a precise
reading of its strength.  Would it work a mile away?  A light year
away?  Does this result follow from QED?  Some equations might be
helpful.

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Sponsor the DES Analytic Crack Project
http://www.cyberspace.org/~enoch/crakfaq.html

Here's a reference to a conference session I just found on the Web.
The presenters claim that prior demonstrations of the A-B effect were
bogus, produced by the magnetic field of the moving particle
interacting directly with the adjacent magnetic field.
 
It also states that no evidence of a magnetic vector potential acting
on a particle in the absence of a magnetic field has ever been
demonstrated.
 
Any comments?
 
-----
 
Session K19 - Magnetic Modeling II.
MIXED session, Wednesday afternoon, March 19
Room 2206, Conv. Center
 
[K19.04] Ehrenberg-Siday-Aharonov-Bohm (ESAB) Effect Has Not Been Observed
 
Gordon R. Freeman, Larry D. Coulson (University of Alberta)
 
The beautiful results from two types of experiment that were claimed
to confirm the existence of the (misnamed) Aharonov-Bohm Effect, with
coherent electrons in split beams (Tonomura amp; co.) and split
conductors (Webb amp; co.), are explained quantitatively by the energy
of interaction of the magnetic field produced by the moving electrons
with the magnetic flux of the adjacent applied field. The electron
velocities (and phases) change by opposite amounts in the two parts of
the split beam, and de Broglie wave interference occurs in the
rejoined beam. No effect of a magnetic vector potential in the absence
of a magnetic field has been demonstrated, so the ESAB Effect has not
been demonstrated to exist.

-- 
Sponsor the DES Analytic Crack Project
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