Aharonov-Bohm effect


Let us consider a magnetic field (B) which is found in a cylinder and only inside the cylinder (Figure 1). In other words, we confine it within a cylinder or we shield it using a cylinder. An electron beam propagates in close proximity to the cylinder. There is no magnetic field outside. Will the electron be influenced? For instance, will it be deflected?

The answer is that it will be deflected although there is no magnetic field. What is the explanation? 

The electron is a particle and a wave. As a particle, it can only sense electromagnetic fields. It is known that electromagnetic fields are derived from electromagnetic potentials. Since the electron is also a wave, which has phase, it can sense electromagnetic potentials, which alter the phase. The change of the phase, and the deflection, are experimentally measurable.

It is noted that electromagnetic potentials, which are called "four-vectors" consist of electric potentials which are scalars and magnetic potentials which are vectors. More details, including tensors, can be found in the corresponding Wikipedia article for the "Electromagnetic potential".

It is important to mention that this means that even under shielding, the electromagnetic potential can be measured and the electromagnetic field can be derived. For instance, a remote measurement of electromagnetic activity would be possible.

Video lecture on the Aharonov-Bohm effect: https://youtu.be/1P68eba7zEs.

Figure 1: From https://commons.wikimedia.org/wiki/File:AharonovBohmEffect.svg. Credit: Kismalac, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons

Measurement of magnetic flux using the Aharonov-Bohm effect

In order to measure very weak magnetic fields and literally non-existent ones, we can use sensors based on the Aharonov-Bohm effect. Such an application related to magnetic field imaging using the tomographic modality is described in this publication:

Valagiannopoulos CA, Marengo EA, Dimakis AG, Alù A. Aharonov–Bohm‐inspired tomographic imaging via compressive sensing. Iet Microwaves Antennas & Propagation. 2018;12(12):1890-1894. doi:https://doi.org/10.1049/iet-map.2017.0609

As mentioned previously, the electron is a particle and a wave. Given that it is a wave, it has phase.  The phase is influenced by the electromagnetic potential and can be experimentally measured to calculate the magnetic flux.

Let us consider Figure 1a of this publication. Practically, if we want to measure in the cloud-like area of the figure, we use two electron beams and we compare the change in phase between:

1) the one which passes from the the cloud-like area, i.e. electron beam 1 and

2) another which passes further away, i.e. electron beam 2.

It is proven, that the electrons will experience a phase shift due to the magnetic flux through area S, i.e. through the area defined by the two paths. Mathematically this equals the integral along the closed loop formed by the two paths.

Lockheed Martin's AB sensor (Aharonov-Bohm), a quantum sensor which is a million times more sensitive than conventional sensors

(detecting signals that are six orders of magnitude weaker) 

Patent: https://patents.google.com/patent/US8389948B2/en

The "AB sensor may pick up intelligence signals from electronically hardened, well protected adversary assets hundreds of miles away. AB sensor may also be used for non-invasive hardware diagnosis."

"Furthermore, AB sensor may be so sensitive that it can detect waves emanating from a human's nerve system." 

Based on "distribution of currents", "the brain can be mapped out".

"Once the nature of the desired signal is determined, AB sensor may be tuned and filters may be used to get rid of unwanted signals (noise). In one example, signals emanating from a nerve system may be so low in frequency (e.g., within the kilohertz range) that a quasi-static approximation, involving magnetic field only, is fully adequate. This may reject 99.5% of the ambient noise in normal environments. An amplitude filter may further reduce the noise to less than 1/10 of 1% (<0.001)."

"In some aspects, using the inverse AB effect where the passage of a beam of charged particles may modify the phase of an alternating magnetic or electrical field, communications may be decoded or altered (e.g., applications in decoding or altering adversary's radio communications)."


Principle of operation: An electron beam is deflected and has its phase changed due to the presence of a signal, and specifically due a vector potential of the signal even if the fields of the signal are zero, due to geometrical characteristics.

In quantum mechanics, particles are waves and have phases. Phase modulation sensors are contrasted to conventional sensors.

"The angular phase of a particle inside a vector potential of a signal can change even if the actual fields embodying the signal are zero". This "may be based solely on geometrical characteristics of the signal." 

Proposed explanation: Let us consider that a signal consists of two electromagnetic waves of opposing phase which cancel out due to destructive interference. Although the fields embodying the signal are zero due to geometry, the energy of the waves is not lost.

Principle of operation - detailed: "An AB sensor is provided that utilizes two coherent beams of electrons, wherein the phase of one of the beams may be shifted as a result of the presence of a signal to be detected. This phase shift may be proportional to the magnitude of the signal to be detected."

"The second electron beam is modulated based on the phase shift of the first wave. Method 900 also comprises detecting the signal based on the modulation of the second electron beam (S910)."

Applications: "Applications of the AB sensor may include spy-craft applications, non-invasive behind-the-wall observation, remote sensing, high frequency and very high frequency direction finding, small antenna applications for low radio frequency, and other suitable applications."

Sensitivity: "The level of sensitivity afforded by the AB sensor is due in part to the fact that the AB effect deals with potentials and not fields. Fields are local entities specific to a point. Potentials, on the other hand, are extended entities influenced by the entire system. The information contained in potentials may include phase information, which may be what distinguishes quantum mechanics from classical mechanics."

Phase modulation "does not necessarily involve energy exchange. While physical phase modulations may involve energy exchange and suffer from the limiting aspects described above, geometrical phase modulations do not necessarily involve energy exchange." 

"Conventional EM sensors may measure electric field, magnetic field, the product of the two fields (e.g., Pointing vector), or the time derivatives thereof. In these cases, the quantity being sensed is a field, or a combination of fields."

"Fields are derivatives of potentials, and are local quantities. Fields contain the information about a single point at a single time. In order to collect information for an extended area, many measurements may need to be taken. On the other hand, phase modulating sensors such as an AB sensor do not necessarily need fields to operate. These sensors may sense potentials, a quantity representative of a space and not a point."

"In quantum mechanics, entities may be considered waves and have phases. In classical mechanics, particles are approximated by points with no phase or extension."

"The phase acquired by a charged particle moving in a magnetic vector potential is a function of the potential and in SI units, is given by" equation 1.

"To measure a phase shift of a particular wave, the wave is contrasted with another wave whose phase is known." "Beam splitting may be used to produce two coherent beams of identical phase. One beam may be exposed to the medium being sensed while keeping the other beam away from the medium."

"AB sensor 100 may be miniaturized for various intelligence applications. For example, AB sensor 100 may be less than a size of a cell phone or a coin depending on the application. AB sensor 100 may also be powered by any suitable energy harvesting means, such as being powered off of ambient EM radiations."

"AB sensor may be so sensitive that it can detect waves emanating from a human's nerve system. Thus, a person's mind may be read without the person realizing it. Based on the direction and strength of a signal, distribution of currents (e.g., thoughts) in the brain can be mapped out."