Polarization‐Locked Floquet Higher‐Order Topological Insulators in Synthetic Dimension

Abstract Floquet engineering provides a powerful tool for exploring topological physics. Systems incorporating Floquet driving can exhibit intriguing topological phenomena without correspondence with static counterparts. Recently, following the development of higher‐order topology, Floquet higher‐order topological insulators have drawn great attention since its peculiarity in the band structure and topological states. Here the higher‐order topological insulator is theoretically demonstrated via Floquet engineering in synthetic frequency dimension. To this end, a 1D Floquet topological insulator is first constructed by introducing periodic driving to the frequency lattice, and the corresponding 0 and π edge states are demonstrated. On this basis, a Floquet higher‐order topological insulator supporting 0 and π corner states is realized by stacking the chains of the 1D Floquet topological insulators with dimerized couplings. Particularly, it is found that the distributions of 0 and π modes occupy the frequency lattices with orthogonal polarizations, which indicate polarization‐locked topological states and enable selective excitation of the topological edge/corner states with specific polarizations. This work lays the foundation for realizing controllable Floquet systems and opens an avenue for exploring higher‐order topological physics with synthetic dimension, which shows great promise for applications in polarization conversion and quantum information processing.