One very bizarre thing that we learn from quantum mechanics is that it is possible for an object to be in a superposition of two or more states at once. For example, in our experiment we will use optical transitions driven by pairs of laser beams to put strontium ions into a superposition state in which the ion is essentially in two different places at the same time. Quantum mechanics also tells us, however, that if you look to see what state an object is in, the process of measuring will collapse the system into a single state. So, although we will be able to "split" ions and put them in two different physical locations at the same time, we will never be able to detect them at two different locations at the same time.
The fact that we can never actually "see" the ions in two places at once might make it sound like there is no point in doing the experiment. But there is a trick to making this superposition useful. What we will do, as has been done in neutral atom interferometers, is to put the two pieces back together, such that each ion is in a single location, before measuring its state. When we put the pieces back together, the ions will "remember" things it felt at both of the locations they occupied when they were in the superposition state, and that "memory" will affect the internal state of the ions when the pieces are put back together again.
Because ions are very sensitive to electric fields, the state that the ions end up in will be determined in part by the difference in the electrostatic potentials at the different locations that the ions experienced. Using laser fluorescence to probe the state of the ions at the end of the experiment, we should be able to detect electric fields with unprecedented precision. This will allow us to do fundamental tests of the laws of electromagnetism - to see if there are perhaps some subtle differences between nature's laws and our mathematical description of them. We will also be able to probe electric fields above surfaces coherently, allowing us to study things like scattering of electron pairs in superconductors.
