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

TL;DR

This paper explores how memory effects in periodically driven quantum systems create topological boundary states in synthetic dimensions, enabling potential applications like optical isolators.

Contribution

It demonstrates that memory-dependent dynamics induce topological edge states in synthetic dimensions of Floquet systems, advancing understanding of topological phases in driven quantum systems.

Findings

Memory effects generate topological boundary states.

Edge states enable directional light transmission.

Physical example illustrating the phenomena.

Abstract

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.