Aharonov–Bohm effect
[1] The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wave function, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments.
[2] There are also magnetic Aharonov–Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested.
Electromagnetic phenomena were elucidated by a series of experiments involving the measurement of forces between charges, currents and magnets in various configurations.
The three issues are: Because of reasons like these, the Aharonov–Bohm effect was chosen by the New Scientist magazine as one of the "seven wonders of the quantum world".
[9] Chen-Ning Yang considered the Aharonov–Bohm effect to be the only direct experimental proof of the gauge principle.
Conversely, the Maxwell fields[vague] under describe the physics, as they do not predict the Aharonov-Bohm effect.
[10][11] It is generally argued that the Aharonov–Bohm effect illustrates the physicality of electromagnetic potentials, Φ and A, in quantum mechanics.
However, Vaidman has challenged this interpretation by showing that the Aharonov–Bohm effect can be explained without the use of potentials so long as one gives a full quantum mechanical treatment to the source charges that produce the electromagnetic field.
[13] Two papers published in the journal Physical Review A in 2017 have demonstrated a quantum mechanical solution for the system.
Thus the Aharonov–Bohm effect validates the view that forces are an incomplete way to formulate physics, and potential energies must be used instead.
In contrast, when using just the four-potential, the effect only depends on the potential in the region where the test particle is allowed.
This is interesting because, while you can calculate the electromagnetic field from the four-potential, due to gauge freedom the reverse is not true.
An ideal solenoid (i.e. infinitely long and with a perfectly uniform current distribution) encloses a magnetic field
(This idealization simplifies the analysis but it's important to realize that the Aharonov-Bohm effect does not rely on it, provided the magnetic flux returns outside the electron paths, for example if one path goes through a toroidal solenoid and the other around it, and the solenoid is shielded so that it produces no external magnetic field.)
The superconducting flux quantum was actually predicted prior to Aharonov and Bohm, by F. London in 1948 using a phenomenological model.
[19] The first claimed experimental confirmation was by Robert G. Chambers in 1960,[20][21] in an electron interferometer with a magnetic field produced by a thin iron whisker, and other early work is summarized in Olariu and Popèscu (1984).
[22] However, subsequent authors questioned the validity of several of these early results because the electrons may not have been completely shielded from the magnetic fields.
[23][24][25][26][27] An early experiment in which an unambiguous Aharonov–Bohm effect was observed by completely excluding the magnetic field from the electron path (with the help of a superconducting film) was performed by Tonomura et al. in 1986.
Thus, assuming the absence of an infinite-range scattering effect by this arbitrary choice of singularity, the requirement of single-valued wave functions (as above) necessitates charge-quantization.
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.
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 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.
[39][40] 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.
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.
In both cases the phase shift was observed via an interference pattern which was also different depending if going forwards and backwards in time.
[48] Application of these rings used as light capacitors or buffers includes photonic computing and communications technology.
[52] Several experiments, including some reported in 2012,[53] 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).
This means that it is physically more natural to describe wave "functions", in the language of differential geometry, as sections in a complex line bundle with a hermitian metric and a U(1)-connection
The monodromy of the connection for a loop going round once (winding number 1) is the phase difference of a particle interfering by propagating left and right of the superconducting tube containing the magnetic field.
For example, in classical statistical physics, quantization of a molecular motor motion in a stochastic environment can be interpreted as an Aharonov–Bohm effect induced by a gauge field acting in the space of control parameters.
