@dga471 is this similar to your work? The article mentions the charge density - does this mean we can actually measure the charge of an electron as being spread out in space? I’m curious if this deals only with non-relativistic QM or if it is sensitive to QFT-level effects as well.
This is more about quantum dots rather than electrons in general. A quantum dot is a small nanometer scale particle that has a few mobile electrons on it. By applying electric and magnetic fields you can control the behavior of the electron(s). The whole system collectively behaves like an atom with a “natural” nucleus and orbiting electrons, leading it to be called an “artificial atom”. As can be seen in the paper, this research is about experimentally testing the theoretical models for characterizing quantum dots, which can potentially make people able to better control them - in line with one of the main proposed applications for QDs, which is quantum computing.
So to answer your question, this is more about condensed matter physics (and reading the theory paper, it seems mostly regular QM). As far as I can tell, there is not yet any proposal for using QDs for fundamental physics. I’m not sure why, but one guess is that QDs are too macroscopic to tease out the tiny effects that are interesting for particle physics.
However, my research does use atoms for fundamental physics - only they are natural rather than artificial atoms. In my case, you have electrons orbiting a molecule consisting of two atoms, which subject the electrons to a very strong electric field that amplify the tiny effects that are relevant to fundamental physics. In order to understand the relationship between the energy levels of the molecule and the fundamental properties of the electrons which are in the molecule, you need to figure out some bread-and-butter molecular physics theory analogous to what is done in this study with QDs. For our case, this is done mainly by specialist molecular theorists in France and Russia - my lab only does the experimental part.
There is a different kind of artificial atom, however, which is very relevant to fundamental physics - geonium, which is what you get when you trap a single electron, proton, or ion with a clever combination of electric and magnetic fields (also known as a Penning trap). The electric and magnetic fields create a ladder of quantum states for the electron, effectively forming an artificial atom where the “nucleus” are the instruments in the lab and the “orbiting” electron is in the middle - a reversal of natural atoms! It is called “geonium” as it is a single electron bound to the earth. This method has been very successful to study a fundamental properties of the electron - its magnetic moment, which is the most precisely measured quantity in all of physics to date.