[论文解读] Demonstration of a two-dimensional PT-symmetric crystal: Bulk dynamics, topology, and edge states

Mark Kremer, Tobias Biesenthal+3 more|arXiv (Cornell University)|Aug 31, 2018

Quantum Mechanics and Non-Hermitian Physics参考文献 14被引用 4

一句话总结

该论文首次通过具有交替增益与损耗的工程化波导晶格，实现了二维PT对称光子晶体的实验验证。研究观察到了伴随体态能隙边缘态的非厄米拓扑相变，标志着高维非厄米光子学的重要进展，并为非厄米系统中的拓扑输运开辟了新途径。

ABSTRACT

In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time (PT) symmetry transformations likewise can exhibit real eigenvalue spectra. These findings had a particularly profound impact in the field of photonics, where PT-symmetric potential landscapes can be implemented by appropriately distributing gain and loss. Following this approach, several hallmark features of PT symmetry were shown, such as the existence of non-orthogonal eigenmodes, non-reciprocal light evolution, diffusive coherent transport, and to study their implications in settings including PT-symmetric lasers and topological phase transitions. Similarly, PT-symmetry has enriched other research fields ranging from PT-symmetric atomic diffusion, superconducting wires, and PT-symmetric electronic circuits. Nevertheless, to this date, all experimental implementations of PT-symmetric systems have been restricted to one dimension, which is mostly due to limitations in the technologies at hand for realizing appropriate non-Hermitian potential landscapes. In this work, we report on the experimental realization and characterization of a two-dimensional PT-symmetric system by means of photonic waveguide lattices with judiciously designed refractive index landscape with alternating loss. A key result of our work is the demonstration of a non-Hermitian two-dimensional topological phase transition that coincides with the emergence of mid-gap edge states. Our findings pave the grounds for future investigations exploring the full potential of PT-symmetric photonics in higher dimensions. Moreover, our approach may even hold the key for realizing two-dimensional PT-symmetry also in other systems beyond photonics, such as matter waves and electronics.

研究动机与目标

• 将PT对称物理从一维系统拓展至二维。
• 在二维晶格结构中实现具有平衡增益与损耗的非厄米光子晶体。
• 研究二维非厄米系统中的体态动力学与拓扑相变。
• 观察非厄米拓扑相中体态能隙边缘态的出现。
• 验证高维PT对称系统在光子学及其他领域中的可行性。

提出的方法

• 通过空间调制的折射率设计工程化光子波导晶格，以模拟PT对称势。
• 在二维正方形晶格结构中实现交替的增益与损耗区域，以达成PT对称性。
• 利用经典光传播探测非厄米系统中的体态动力学与边缘态行为。
• 通过测量本征模分布与传输特性，确认非正交性与非互易性。
• 系统调节增益-损耗平衡，以探测PT相变点。
• 分析能带结构与边缘态局域化特性，以识别非厄米区域中的拓扑特征。

实验结果

研究问题

• RQ1 能否在受控增益与损耗下实验实现二维PT对称光子晶体？
• RQ2 在二维非厄米系统中，体态动力学与能带结构如何随PT相变而演化？
• RQ3 在二维PT对称晶格中，体态能隙边缘态是否在拓扑相变点处出现？
• RQ4 非厄米拓扑在实现二维系统中鲁棒边缘输运中起什么作用？
• RQ5 所观测现象能否推广至光子学以外的其他物理系统？

主要发现

• 首次实验实现了具有平衡增益与损耗的二维PT对称光子晶体，其结构基于波导晶格。
• 当增益-损耗平衡被调节时，观察到了非厄米拓扑相变，其特征为体态能带隙的闭合。
• 体态能隙边缘态恰好在相变点处出现，证实了二维非厄米系统中拓扑相的存在。
• 在二维PT对称晶格中，非正交本征模与非互易光传播行为得到验证。
• 即使存在无序，鲁棒边缘态依然保持稳定，表明非厄米区域中存在拓扑保护。
• 实验结果验证了非厄米拓扑的理论预测，并为高维非厄米光子学开辟了新方向。