5.7 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Aharonov–Bohm effect | 4/5 | https://en.wikipedia.org/wiki/Aharonov–Bohm_effect | reference | science, encyclopedia | 2026-05-05T10:54:30.845762+00:00 | kb-cron |
== Electric effect == Just as the phase of the wave function depends upon the magnetic vector potential, it also depends upon the scalar electric potential. By constructing a situation in which the electrostatic potential varies for two paths of a particle, through regions of zero electric field, an observable Aharonov–Bohm interference phenomenon from the phase shift has been predicted; again, the absence of an electric field means that, classically, there would be no effect. From the Schrödinger equation, the phase of an eigenfunction with energy
E
{\displaystyle E}
goes as
e
−
i
E
t
/
ℏ
{\displaystyle e^{-iEt/\hbar }}
. The energy, however, will depend upon the electrostatic potential
V
{\displaystyle V}
for a particle with charge
q
{\displaystyle q}
. In particular, for a region with constant potential
V
{\displaystyle V}
(zero field), the electric potential energy
q
V
{\displaystyle qV}
is simply added to
E
{\displaystyle E}
, resulting in a phase shift:
Δ
φ
=
−
q
V
t
ℏ
,
{\displaystyle \Delta \varphi =-{\frac {qVt}{\hbar }},}
where t is the time spent in the potential. For example, we may have a pair of large flat conductors, connected to a battery of voltage
Δ
V
{\displaystyle \Delta V}
. Then, we can run a single electron double-slit experiment, with the two slits on the two sides of the pair of conductors. If the electron takes time
t
{\displaystyle t}
to hit the screen, then we should observe a phase shift
e
Δ
V
t
/
ℏ
{\displaystyle e\Delta Vt/\hbar }
. By adjusting the battery voltage, we can horizontally shift the interference pattern on the screen. The initial theoretical proposal for this effect suggested an experiment where charges pass through conducting cylinders along two paths, which shield the particles from external electric fields in the regions where they travel, but still allow a time dependent potential to be applied by charging the cylinders. This proved difficult to realize, however. Instead, a different experiment was proposed involving a ring geometry interrupted by tunnel barriers, with a constant bias voltage V relating the potentials of the two halves of the ring. This situation results in an Aharonov–Bohm phase shift as above, and was observed experimentally in 1998, albeit in a setup where the charges do traverse the electric field generated by the bias voltage. The original time dependent electric Aharonov–Bohm effect has not yet found experimental verification.
== Gravitational effect ==
The Aharonov–Bohm phase shift due to the gravitational potential should also be possible to observe in theory, and in early 2022 an experiment was carried out to observe it based on an experimental design from 2012. In the experiment, ultra-cold rubidium atoms in superposition were launched vertically inside a vacuum tube and split with a laser so that one part would go higher than the other and then recombined back. Outside of the chamber at the top sits an axially symmetric mass that changes the gravitational potential. Thus, the part that goes higher should experience a greater change which manifests as an interference pattern when the wave packets recombine resulting in a measurable phase shift. Evidence of a match between the measurements and the predictions was found by the team. Multiple other tests have been proposed.
== Non-abelian effect == In 1975 Tai-Tsun Wu and Chen-Ning Yang formulated the non-abelian Aharonov–Bohm effect, and in 2019 this was experimentally reported in a system with light waves rather than the electron wave function. The effect was produced in two different ways. In one light went through a crystal in strong magnetic field and in another light was modulated using time-varying electrical signals. In both cases the phase shift was observed via an interference pattern which was also different depending if going forwards and backwards in time.
== Aharonov–Bohm nano rings == Nano rings were created by accident while intending to make quantum dots. They have interesting optical properties associated with excitons and the Aharonov–Bohm effect. Application of these rings used as light capacitors or buffers includes photonic computing and communications technology. Analysis and measurement of geometric phases in mesoscopic rings is ongoing. It is even suggested they could be used to make a form of slow glass. Several experiments, including some reported in 2012, show Aharonov–Bohm oscillations in charge density wave (CDW) current versus magnetic flux, of dominant period h/2e through CDW rings up to 85 μm in circumference above 77 K. This behavior is similar to that of the superconducting quantum interference devices (see SQUID).
== Mathematical interpretation ==