Creating higher-order topological phases using synthetic dimensions in dynamically modulated ring resonators

Abstract

Higher-order topological insulators (HOTIs), originating from quantized quadrupole and octupole moments, have attracted significant interest since they support boundary states that are two or more dimensions lower than their bulk. However, previous HOTIs have been restricted to real-space dimensions. Here we construct photonic HOTIs using synthetic dimensions, comprising frequency modes of dynamically modulated rings. We show how quadrupole and octupole HOTIs supporting topologically protected corner modes emerge in a lattice of modulated photonic molecules and predict a dynamical topological phase transition in this system. Additionally, we propose a quantized hexadecapole (16-pole) insulator by leveraging synthetic dimensions to create a 4D hypercubic lattice that cannot be realized in real space.