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COL Hightlight (Vol. 19, Iss. 4): 拓扑与集成的碰撞:得见能谱调控的火花

发布:lina000288阅读:595时间:2021-4-15 09:25:35

拓扑与集成的碰撞:得见能谱调控的火花

 

近年来,拓扑绝缘体的研究蓬勃兴起,由于光学拓扑绝缘体的表面态具有对缺陷和障碍物免疫的特性,其抗干扰传输性能受到了极大的关注。

凭借对时间维度的动态调控,拓扑系统中发展出含时驱动系统。这种具备动态调制能力的拓扑绝缘体统称为弗洛凯拓扑绝缘体(Floquet topological insulators , FTIs)。通过调制FTIs驱动的频率、强度振幅和对称性等参量,可以更加充分地研究拓扑效应及开发相关应用。目前在冷原子、光子晶体等体系中已有可动态调控能带结构的FTIs,然而如何直观有效地观察含时驱动系统中FTIs能带结构变化与拓扑态传输关联性质,仍然是有待研究人员突破的方向。

光Floquet拓扑绝缘体示意图(源自“诺奖视点:拓扑走进光学”)

由于光子晶体的周期性结构在数学形式上与量子力学的薛定谔方程具有相似性,近年来用光场传播物理系统来模拟电子波函数的演化行为成为研究趋势,其中波导阵列凭借其稳健性和对缺陷、杂质的免疫性得到了很多研究人员的关注。利用FTIs的模拟研究,可在波导阵列传播方向上引入调制形成周期性弯曲的波导阵列,其中可调控的参数包括弯曲频率、弯曲幅度和波导间距等。

研究人员已经在弯曲波导阵列中模拟了布洛赫振荡、动态局域化和无质量狄拉克粒子演化等量子现象,并进一步利用FTIs设计对应的弯曲波导阵列,有望揭示含时驱动的拓扑态的形成机制。然而目前并没有清晰的系统来揭示能谱结构与驱动周期之间的关系。

上海理工大学的程庆庆研究团队联合南京大学王怀强研究员将微波频段推广至近红外频段,并搭建了含时驱动硅基波导阵列系统,借由驱动系统的周期变化,观察了能带带隙开闭和重新开启的全过程。相关研究成果发表在Chinese Optics Letters第19卷第4期上(Yu, Ye, et al., Floquet spectrum and optical behaviors in dynamic Su–Schrieffer–Heeger modeled waveguide array)。

SSH模型可调控的弯曲波导阵列

在该团队2019年 PRL的成果之上,文章进一步阐明了高频驱动波导与静态波导之间的等价性,由高频驱动波导搭建Su–Schrieffer–Heeger(SSH)模型,并在实验上观察到等价的拓扑零模和拓扑零模的耦合效应。此工作实现了Floquet一维动态SSH模型中弯曲调制的硅波导阵列,这为“按需”构建可视化FTIs模拟平台提供了一种新的途径。

该工作获得了国家自然基金面上项目(编号:11874266)和青年科学基金项目(编号:11604208)的支持。

 

Floquet spectrum and optical behaviors in dynamic Su–Schrieffer–Heeger modeled waveguide array

 

In the development of topological photonics, robust propagation behaviors of topologically protected states in photonic analog of topological insulators have attracted broad attention. In the presence of dynamic time-dependent drivings, much more interesting topological phenomena are expected. Specifically, when the driving field is time-periodic, dynamic analogs of topological insulators, Floquet topological insulators FTIs, have been theoretically proposed in various dimensions. On the experimental side, researchers have already designed FTIs in cold atoms, photonic crystals and other systems. However, clear demonstrations of dynamic behaviors of FTIs have been rare, especially in one-dimensional systems, due to the lack of a flexible platform with easily tunable frequency and amplitude of the periodic driving field.

Illustration of Floquet topological insulators (source from "诺奖视点:拓扑走进光学")

Recently a variety of physical systems have been developed using coupled-mode equations to describe the propagation of light fields to imitate the evolution of electronic wave functions described by the Schrodinger equation, among which waveguide arrays have attracted intense interest. Notably, by treating the propagation direction as the time dimension, periodic modulations can be genuinely introduced by periodically bending the waveguides, with easily tunable structural parameters of bending frequency, bending amplitude, and waveguide spacings. This enables us to realize FTIs and demonstrate corresponding exotic dynamic topological propagation behaviors in waveguide systems.

Researchers have observed an anomalous edge localized mode exhibiting periodically oscillating behaviors at moderate frequencies, which was theoretically confirmed as the long-sought Floquet π mode (PRL 2019). However, a more detailed Floquet band gap evolution and the equivalence between high frequency driven waveguide and static waveguide have not been fully revealed in the work.

Cheng Qingqing and collaborator (Wang Huaiqiang at Nanjing University), further extended the microwave to the near-infrared frequency, and built a time-dependent driving system for silicon-based waveguide array. By adjusting the frequency of the periodic driving, a complete evolution of the Floquet band gap was observed in the whole process of opening, closing and reopening. The result was published in Chinese Optics Letters, Vol. 19, Iss. 4. (Yu Ye, et al., Floquet spectrum and optical behaviors in dynamic Su–Schrieffer–Heeger modeled waveguide array).

SSH model of the bend-modulated waveguide array

This work clearly demonstrates the equivalence between high frequency driven waveguide and static waveguide. They further built an analog of static SSH (Su–Schrieffer–Heeger) model with high frequency driven waveguides, and observed the topologically equivalent zero mode and related coupling effects. This work realizes the bend-modulated silicon waveguide array obeying the Floquet one-dimensional dynamic SSH model, which provides a versatile platform for Floquet engineering designed "on-demand".

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874266, 11604208)