Abstract
Conventional topological insulators support boundary states with dimension one lower than that of 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 with dimensions two or more lower than that of 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 (PHOTIs) 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 adjacent 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 fourth-order hexadecapole (16-pole) insulator supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.
Highlights
Introduction A conventional topological insulator in2D and 3D supports gapless edge states and surface states, respectively, that are protected against local perturbations by the nontrivial topology of the bulk
A 1D array of modulated photonic molecules forms a quadrupole photonic higher-order topological insulators (PHOTIs) in the synthetic frequency dimension, in which we show the excitation of topologically nontrivial corner modes
Octupole and hexadecapole insulators we show how the concept of synthetic dimensions can be exploited to construct PHOTIs of even higher order, such as an octupole insulator in a 3D cubic lattice and a hexadecapole (16-pole) insulator in a 4D hypercubic lattice supporting corner modes with a b
Summary
Introduction A conventional topological insulator in2D and 3D supports gapless edge states and surface states, respectively, that are protected against local perturbations by the nontrivial topology of the bulk. By antisymmetrically modulating the two rings in a photonic molecule at the frequency spacing between the ring modes, we realize a lattice along the synthetic frequency dimension. A 1D array of modulated photonic molecules forms a quadrupole PHOTI in the synthetic frequency dimension, in which we show the excitation of topologically nontrivial corner modes.
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