Higher-order topological insulators in synthetic dimensions

TL;DR

This paper introduces photonic higher-order topological insulators in synthetic dimensions, demonstrating topologically protected corner modes and phase transitions, and extends the concept to realize higher multipole moments like hexadecapoles in synthetic 4D lattices.

Contribution

The work constructs photonic higher-order topological insulators in synthetic dimensions, enabling realization of complex topological states and higher multipole moments beyond real-space limitations.

Findings

Demonstration of quadrupole PHOTI with protected corner modes

Prediction of dynamical topological phase transitions

Realization of 4th order hexadecapole insulator in synthetic 4D lattice

Abstract

Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order topological insulators have been proposed as a way of realizing topological states that are two or more dimensions lower than the bulk, due to the quantization of bulk quadrupole or octupole moments. However, all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here we construct photonic higher-order topological insulators (PHOTI) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension, where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacently coupled photonic molecules, we predict a dynamical topological phase transition in the PHOTI. Furthermore, we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a 4th order hexadecapole (16-pole) insulator, supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.