Historical research guide · 0525 · 2023
Electrodynamic Aharonov-Bohm effect
Pablo L. Saldanha
In one minute
Pablo Saldanha, at the Federal University of Minas Gerais, proposes a new version of one of the most surprising confirmed effects in physics. In the Aharonov-Bohm effect an electron’s interference pattern shifts because of a magnetic flux it never touches: the potentials, not the fields, set its phase. Saldanha takes even that away. In his scheme the two arms of the interferometer enclose no magnetic flux at all, and while the electron is in a superposition inside two Faraday cages that keep every field it could feel negligible, the current in a nearby solenoid is ramped. He shows the phase difference between the two arms is in general still not zero, and that it comes from the change in the vector potential during the flight rather than from any scalar potential. He then rebuilds the topological account in spacetime instead of space: the phase equals the electric and magnetic flux through a spacetime surface bounded by the particle’s two possible histories, gauge-invariant and independent of which surface you draw.
Connection
Chapter 10 rests on the fact that the vector potential is physical and that what it controls is phase; this paper pushes that to its sharpest form, where the phase is set purely by how the potential changes in time while the particle feels no force at all. For chapter 1 it is a clean rung on the evidence ladder: a named, published, gauge-invariant prediction with an interferometer that already exists and a stated way to test it.
From the source
In the magnetic Aharonov-Bohm effect the interference pattern of a quantum charged particle depends on the magnetic flux enclosed by the two interferometer paths even though the particle propagates only through regions where the electromagnetic fields are null; the phase difference is the particle charge times that flux divided by h-bar. This contradicts the notion that a charge is affected only by the local fields, and it has been observed in many different systems.Introduction, paragraphs 1 to 2; Equation 2
Saldanha proposes an electrodynamic scheme in which a nonzero Aharonov-Bohm phase difference appears even though the interferometer paths enclose no magnetic flux and the two arms are subject to a negligible scalar potential difference: the solenoid sits outside the interferometer and its current is changed while the particle is in a superposition inside two Faraday cages, so the particle is always subject to negligible electromagnetic fields.Abstract; Figure 3(a); Equation 5
The surviving phase term is the circulation of the change in the vector potential. Because the vector potential changes during the particle’s flight, that circulation is nonzero from the wave packet’s point of view, which makes the effect distinct from the ordinary electric Aharonov-Bohm effect, where both the phase and the relevant electric field come from a scalar potential.Discussion following Equation 5, third paragraph
All three cases fold into one explicitly gauge-invariant formula: the phase difference is the particle charge divided by h-bar, times the magnetic flux through a spacetime surface bounded by the two possible particle trajectories, minus the corresponding electric term integrated over the same surface. The magnetic and the electric Aharonov-Bohm effects are particular cases of it.Equation 6 and the paragraph introducing it
The effect remains topological once the accounting is done in spacetime rather than in space alone: Saldanha shows that two different deformations of one trajectory into the other give phase contributions that differ by the change in solenoid flux from one term and cancel it with the other, so the answer depends only on the topology of the spacetime region where the fields are null and on which hole each possible trajectory passes through.Equation 8 and the surrounding argument, Figures 3(b) and 3(c)
What to watch: the test. Electron Mach-Zehnder interferometers already exist for electrons in free space and in material media, and Saldanha’s proposal is to add Faraday cages to the arms and time-correlate the solenoid current ramp with the electron arrivals. A measured phase shift would confirm that the Aharonov-Bohm phase is acquired continuously during propagation, as quantum-electrodynamic treatments predict.Closing section on electronic Mach-Zehnder interferometers; paragraph citing the quantum electrodynamics treatments
The way in
https://doi.org/10.1103/PhysRevA.108.062218How to cite it
Pablo L. Saldanha (2023) Electrodynamic Aharonov-Bohm effect doi:10.1103/PhysRevA.108.062218