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提出一种基于超导传输线腔的一维晶格理论方案, 其中包含两种超导微波腔系统. 通过调控磁通量子比特来操纵临近和次临近晶胞之间的相互作用, 使其获得集体动力学演化规律, 来研究其中的拓扑特性. 首先, 分析了奇偶晶格数目的能谱和边缘状态, 发现奇偶晶格数将会影响系统的拓扑特性, 并且边缘状态分布发生翻转过程. 其次, 在次临近的相互作用下, 发现其相互作用存在相互制约现象, 通过调控其相互作用, 可以实现系统拓扑相变和拓扑量子态的传递过程. 最后, 研究了缺陷对拓扑特性的影响, 发现缺陷势能较小时, 系统能带变化周期稳定, 边缘态保持不变, 能谱产生微小波动, 并且可以区分; 缺陷势能较大时, 能带分布被破坏, 将会变得无序和混乱. 根据本文的研究结果, 可以设计一些新型量子器件, 应用在量子光学和量子信息处理中.We propose a theoretical scheme for a one-dimensional lattice based on a superconducting quantum circuit system consisting of two types of superconducting microwave cavities, the interaction between nearest-neighbor and next-nearest-neighbor unit cells that can be adjusted by the magnetic flux, the system can obtain the collective dynamic evolution and study the topological properties of the system.First, we investigate the energy spectrum and edge states of the odd-even lattice size and find that the odd-even lattice number affects the topological properties of the system. Furthermore, considering the next-nearest interactions, it is found that there are constraints on the next-nearest interactions, which can be tuned to study the topological phase transitions of the system and the transfer of topological quantum states.In addition, considering the influence of defects on topological properties, it is found that the defect potential energy is small, the system energy band is stable, the edge states remain unchanged, and the energy spectrum fluctuation is small and distinguishable. Conversely, the energy band distribution is destroyed, it will become disordered and chaotic. The research results can design some new quantum devices for quantum optics and quantum information processing.
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