Nemirovsky Liat, Cohen Moshe-Ishay, Lumer Yaakov, Lustig Eran, Segev Mordechai
Solid State Institute, and Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Phys Rev Lett. 2021 Aug 27;127(9):093901. doi: 10.1103/PhysRevLett.127.093901.
Synthetic-space topological insulators are topological systems with at least one spatial dimension replaced by a periodic arrangement of modes, in the form of a ladder of energy levels, cavity modes, or some other sequence of modes. Such systems can significantly enrich the physics of topological insulators, in facilitating higher dimensions, nonlocal coupling, and more. Thus far, all synthetic-space topological insulators relied on active modulation to facilitate transport in the synthetic dimensions. Here, we propose dynamically invariant synthetic-space photonic topological insulators: a two-dimensional evolution-invariant photonic structure exhibiting topological properties in synthetic dimensions. This nonmagnetic structure is static, lacking any kind of modulation in the evolution coordinate, yet it displays an effective magnetic field in synthetic space, characterized by a Chern number of one. We study the evolution of topological states along the edge, and on the interface between two such structures with opposite synthetic-space chirality, and demonstrate their robust unidirectional propagation in the presence of defects and disorder. Such topological structures can be realized in photonics and cold atoms and provide a fundamentally new mechanism for topological insulators.
合成空间拓扑绝缘体是一种拓扑系统，其中至少一个空间维度被模式的周期性排列所取代，这些模式呈能级阶梯、腔模或其他某种模式序列的形式。这类系统能够显著丰富拓扑绝缘体的物理内涵，有助于实现更高维度、非局域耦合等等。到目前为止，所有合成空间拓扑绝缘体都依赖主动调制来促进在合成维度中的输运。在此，我们提出动态不变的合成空间光子拓扑绝缘体：一种二维演化不变的光子结构，在合成维度中展现出拓扑性质。这种非磁性结构是静态的，在演化坐标中缺乏任何形式的调制，但它在合成空间中显示出有效磁场，其陈数为1。我们研究了拓扑态沿边缘以及在两个具有相反合成空间手性的此类结构之间的界面上的演化，并证明了它们在存在缺陷和无序的情况下具有稳健的单向传播特性。这种拓扑结构可以在光子学和冷原子中实现，并为拓扑绝缘体提供了一种全新的基本机制。
