Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals

When a d-dimensional quantum system is subjected to a periodic drive, it may be treated as a (d+1)-dimensional system, where the extra dimension is a synthetic one. In this work, we take these ideas to the next level by showing that non-uniform potentials, and particularly edges, in the synthetic dimension are created whenever the dynamics of system has a memory component. We demonstrate that topological states appear on the edges of these synthetic dimensions and can be used as a basis for a wave packet construction. Such systems may act as an optical isolator which allows transmission of light in a directional way. We supplement our ideas by an example of a physical system that shows this type of physics.