Topological state engineering via supersymmetric transformations

TL;DR

This paper explores how supersymmetric transformations can be used to manipulate and reconfigure topological states in photonic systems, enabling controlled phase transitions and protection of topological features.

Contribution

It introduces a novel approach using SUSY transformations for systematic topological state engineering in photonic lattices, supported by theoretical and experimental evidence.

Findings

SUSY transformations can induce phase transitions in topological states.

SUSY can selectively suspend and restore topological protection.

Understanding symmetries guides targeted topological property control.

Abstract

The quest to explore new techniques for the manipulation of topological states simultaneously promotes a deeper understanding of topological physics, and is essential in identifying new ways to harness their unique features. Here, we examine the potential of supersymmetric (SUSY) transformations to systematically address, alter and reconfigure the topological properties of a system. To this end, we theoretically and experimentally study the changes that topologically protected states in photonic lattices undergo as SUSY transformations are applied to their host system. In particular, we show how SUSY-induced phase transitions can selectively suspend and re-establish topological protection of specific states. Furthermore, we reveal how understanding the interplay between internal symmetries and the symmetry constraints of supersymmetric transformations provides a roadmap to directly access the desirable topological properties of a system. Our findings pave the way for establishing SUSY-inspired techniques as a powerful and versatile tool for topological state engineering.