News Resource: School of Physics

Editor: News Agency of BIT

Translator: Wang Wanqing, News Agency of BIT

Recently, Professor Lu Cuicui of the School of Physics of BIT, Professor Hu Xiaoyong and Academician Gong Qihuang of Peking University, Academician Chen Ziting of the Hong Kong University of Science and Technology and others have developed a method to construct effective Hamiltonians for studying the topological optical system of gain-loss domain walls in the study of non-Hermitian topological photonics, revealing the generation mechanism of topological state induced by gain-loss domain walls, published in the authoritative journal of physics, Physiological Review Letters.

Non-Hermitian topological photonic systems have complex physics compared to Hermitian systems. Since most of the open systems in the real world are non-Hermitian systems, the study of non-Hermitian topological photonic systems has important value in terms of foundation, frontier, and application. Under normal circumstances, if the two domains of topological non-trivial and topological trivial are stitched together, a topological boundary state will appear on the domain walls, and the number of topological states corresponds to the difference of the corresponding topological invariants, and the topological invariants can be analyzed by the corresponding system. Studies have shown that even if two topological equivalent domains are spliced together, when the gain/loss difference between the two domains is increased, a local topological boundary state will appear on the domain wall, which cannot be characterized by topological invariants, and because the system does not have translational symmetry, it is impossible to directly use the existing theoretical calculation methods to carry out in-depth research.

In order to give a more universal research method, the research team studied a variety of common non-Hermitian topological photonic systems such as AAH model, SSH model, valley photonic crystal and C6v type photonic crystal, and proposed a new method to construct the effective Hamiltonian amount of the system by introducing the coupling coefficient between different domain topologies, which provides a more universal research scheme for the study of new gain-loss domain wall topological optical systems. In the one-dimensional AAH configuration described by the tightly bound Hamiltonian H_1D, the fitting method is used to determine the relevant parameters of the effective Hamiltonian H_eff, and theoretical calculations find that the effective Hamiltonian H_eff can accurately describe the pattern distribution and pattern frequency of the corresponding topological state (Figure 1). At the same time, the research team generalized the method to high dimension, by constructing a cross-shaped gain-loss interface in the two-dimensional AAH configuration, and also realized the topological angular state induced by the gain-loss domain walls, and successfully constructed an effective Hamiltonians to explain such phenomena, by appropriately adjusting the system parameters and the gain-loss distribution in the system, the topological angular state can be induced at different positions in the two-dimensional system (Figure 2). This work reveals the mechanism of topological state generation induced by the gain-loss domain walls, and has guiding significance for active regulation of topological states.

Figure 1 (a) Coupled terms in an effective Hamiltonian quantity fitted by introducing parameters. (b), (c) Comparison of pattern frequencies and pattern distributions derived from H_1D and H_eff, respectively.

Figure 2 By designing the distribution of gain loss, angular states can be induced at different positions in the two-dimensional system.

Professor Lu Cuicui of BIT, Professor Hu Xiaoyong of Peking University and Academician Chen Ziting of the Hong Kong University of Science and Technology are the co-corresponding authors of the paper, while Li Yandong, a doctoral student at Peking University, and Fan Chongxiao, a graduate of Peking University (now studying at the Max Planck Institute in Germany), are the co-first authors of the paper. This work has been supported by the National Key R&D Program, the National Natural Science Foundation of China, and the Academic Startup Program of The Distinguished Young Scholars of BIT.