Ever since we studied physics or whenever we heard the word ‘Physics’, the things that come first to our mind are Newton’s law, charged particles, electric field, magnetic fields, Maxwell’s equations, and many other theories and phenomenon. But physics is much more and beyond these theories. The Aharonov-Bohm effect is one such interesting phenomenon of quantum physics which explains how a charged particle can deviate from its path.
EXPLANATION OF PHENOMENON
In this phenomenon, an electrically charged particle (a particle that has a charge over it) is affected by an electromagnetic potential despite being confined to an area when both the electric field and the magnetic field becomes zero. This happens when the wave of a charged particle passes around a long solenoid (a solenoid is a coil whose length is greater than its diameter which produces a uniform magnetic field around it), the wave of the charged particles experiences a phase shift as a result of the magnetic field of the solenoid, though the magnetic field being irrelevant in the region through which the particle passes. If solenoid contains no magnetic field, vector potential outside the solenoid is set to zero, so there is a phase shift and thus the interference pattern will depend only on the difference between traveled paths.
When we turn the magnetic field ON, the wave functions will acquire an additional phase. The total phase difference between both the beams will be proportional to the magnetic flux inside the solenoid. So, in a way if we change the magnetic field in the solenoid, we change the phase difference between beams and interference patterns will shift. This is called the Aharonov-Bohm effect. This experiment can somewhat be depicted by double-slit experiment also (according to the double-slit experiment, light and matter can behave both as a wave as well as a particle, the wave nature of light causes the light waves passing through the two slits that are the double slits to interfere, producing bright and dark bands on the screen behind it, a result that would not be the same result if light consisted of classical particles).
The Aharonov–Bohm effect is also called the Ehrenberg–Siday–Aharonov–Bohm effect because Werner Ehrenberg and Raymond E. Siday were the first to predict the effect in the year 1949. Also, Yakir Aharonov and David Bohm published their detailed analysis in 1959. When the effect came up, it had large errors. Many physicists at that time claimed that this effect cannot be measured so experimental confirmation was needed to actually study the experiment and know it’s worth. Aharonov and Bohm when developing their idea also consulted experimental physicist Sir Robert G. Chambers and with his help they described the experiment which had to be carried out to prove this theory, which is also mentioned in their article. A year later, Chambers performed the proposed experiment as written in their article and proved that the effect does exist. By the time in the following years the effect was confirmed by more and more precise experiments so today only a few people still doubt it’s existence otherwise it is studied as a complete physics phenomenon.
When you talk about Aharonov-Bohm effect, you naturally think of a phenomenon that is mainly related to the magnetic field of a solenoid, but in fact, there exist 2 types of the effect for the same phenomenon. In magnetic effect, wavefunctions gain phase difference while traveling due to the field generated by the solenoid which describes the magnetic field, but in the work of Aharonov and Bohm they also described another version of the same phenomenon that is when particles travel through a region where electric field (E) is zero, but the scalar potential is not zero.
SOLENOID MAGNET EXPERIMENT
Robert G. Chambers performed the experiment to prove the Aharonov–Bohm effect. The first problem that he faced in designing the experiment was how to separate electron beams to sufficient distance. If the source is too small, the separation of beams can be random, but in a real experiment, separation of the beam is limited by the finite size of the source. So the beam of electrons used in the experiment by him was produced by an electron microscope. Since the wavelength of the electron was smaller than 1nm (nanometer), which is much smaller than the size of the solenoid, so the diffraction can be neglected. He used electrostatic bi-prism to split the beam into two parts. Bi-prism consists of aluminized quartz fiber and two earthed metal plates. When he performed the experiment, he saw that fringes in fact shifted in the vertical direction, which was clear evidence of the Aharonov-Bohm effect.
Even though Chambers’ experimental results confirmed the predictions of Aharonov and Bohm, some still argued that the effect was not caused by electromagnetic potentials and also argued that the magnetic field leaks out in the region where electrons travel, so many believed that the observed effect could be explained by the interaction of electrons with the magnetic field. Since he could not provide the full and clear result of his experiment to prove the effect so more experiments were needed to indisputably prove the Aharonov-Bohm effect.
Aharonov-Bohm effect has some important practical importance. We saw that phase shift between electron beams strongly depends on magnetic flux that is enclosed within. The effect enables us to measure extremely small differences in magnetic flux. The simplest case of such a magnetometer would be two wires with electron current, forming a closed-loop, and we would count oscillations of current through the structure when magnetic flux through the loop would change.
The Aharonov–Bohm effect is important because it bears 3 major issues apparent in the reforming of (Maxwell’s) classical electromagnetic theory as a gauge theory, which before the introduction of quantum mechanics could be argued upon to only have a mathematical relationship with no reference of physical phenomenon or physics.
The Aharonov–Bohm effect has also been chosen by the New Scientist magazine as one of the “Seven Wonders of the Quantum World”. Despite having faced so many doubts of various scientists, these effects are still undoubtedly one of the remarkable experiments in the world of quantum physics.