Realizing the 4D quantum Hall effect using synthetic dimensions

In recent years, there has been rapid development in control and manipulation of coherent quantum systems. These advances allow for the study and utilization of new coherent quantum phenomena. In my talk, I will introduce our research on studying quantum engineered systems with its ramifications to disorder, out-of-equilibrium drives and dissipation, many-body interactions, and topology, as well as its consequences for fundamental physics and device applications. As an example, I will introduce the notion of synthetic dimensions and how they can be engineered in the lab. Using synthetic dimensions, we have proposed and realized for the first time, the physics of the 4D Hall effect in experiments.