Historical research guide · 0846 · 2007
Macroscopic Test of the Aharonov-Bohm Effect
Adam Caprez · Brett Barwick · Herman Batelaan
In one minute
The Aharonov-Bohm effect is the cleanest evidence that the electromagnetic potential is physically real: an electron passing a shielded magnetic flux shifts its interference fringes even though no field, and so no classical push, ever reaches it. Adam Caprez, Brett Barwick and Herman Batelaan at the University of Nebraska-Lincoln test the second half of that sentence head-on. If a hidden force were secretly doing the work, it would have to shove the electron sideways by just the right amount — and a shove that large would also make the electron arrive late. So they measured the arrival time. A femtosecond laser pulse strips electrons from a sharp tip, the pulse flies between two solenoids joined by iron bars into a square magnetic toroid, and a channelplate records each landing to about a tenth of a nanosecond. As the solenoid current is turned up, the arrival time does not move. The whole class of force explanations is ruled out, and the potential is left holding the result on its own.
Connection
Chapter 10 rests on the vector potential being a real and usable handle on phase rather than a bookkeeping device, and this is the measurement that closes the obvious escape route — there is no hidden force of the right size doing the work. For chapter 1 it is a model rung on the evidence ladder: name the alternative explanation, derive the signature it would leave, then go and look for that signature. Read it with the transverse-deflection experiment at /library/stm-81bc78c3b1, the gauge-invariance proof at /library/stm-9369e78ff5 and the spacetime-topology schemes at /library/stm-1897890324.
From the source
The original Type-I Aharonov-Bohm phase shift exists under experimental conditions where the electromagnetic fields, and therefore the forces, are zero; it is that absence of forces which makes the effect entirely quantum mechanical, and although the phase shift itself has been demonstrated unambiguously, the absence of forces had never been shown.Abstract
Excellent agreement has been found between the measured phase shift and the theoretical prediction that the shift equals the electron charge divided by h-bar, multiplied by the line integral of the vector potential around a contour enclosing the magnetic flux of a solenoid — from Chambers onward, including Tonomura’s toroid experiments.Introduction, Eq. (1)
A semiclassical force can be constructed that reproduces the Aharonov-Bohm phase shift exactly: modelling the solenoid as a stack of current loops, or as a line of magnetic dipoles as Boyer did, the Lorentz forces between the passing electron and the carriers in the coil give a path-length difference whose semiclassical phase equals the flux times the charge divided by h-bar. That coincidence is what makes an experimental test worth doing.Eqs. (5) to (8); Boyer, Found. Phys. 32, 41 (2002)
A displacement large enough to account for the phase shift would also produce a time delay equal to the flux times the charge divided by the electron mass times the square of its velocity, so a time-of-flight measurement can rule out the entire class of semiclassical force theories at once, whatever their internal details.Eq. (4) and the paragraph following it
In the experiment a femtosecond laser pulse extracts electrons from a field-emission tip, the pulse passes between two identical solenoids joined by high-permeability magnet-iron bars into a square magnetic toroid to suppress flux leakage, and arrival is timed with a channelplate; the scatter of the arrival times is about a tenth of a nanosecond, and the same apparatus does register nanosecond-scale electromagnetic effects when the acceleration voltage is changed.Experiment description with Fig. 2; Fig. 4
No time delay is observed as a function of the current through the solenoids, with or without the magnetic shield in place, so there is no force acting on an electron passing a macroscopic solenoid of a magnitude that could explain the Aharonov-Bohm effect, and all force explanations leading to such a delay are ruled out.Results, Fig. 3; Conclusion
The way in
https://doi.org/10.1103/PhysRevLett.99.210401How to cite it
Adam Caprez, Brett Barwick, Herman Batelaan (2007) Macroscopic Test of the Aharonov-Bohm Effect doi:10.1103/PhysRevLett.99.210401