Yu Danying, Peng Bo, Chen Xianfeng, Liu Xiong-Jun, Yuan Luqi
State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China.
Shanghai Research Center for Quantum Sciences, 201315, Shanghai, China.
Light Sci Appl. 2021 Oct 7;10(1):209. doi: 10.1038/s41377-021-00646-y.
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of nonequilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and momentum dimensions. Here, we propose the topological holographic quench dynamics in synthetic dimension, and also show it provides a highly efficient scheme to characterize photonic topological phases. A pseudospin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state, which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is encoded in quench dynamics solely in the time dimension, and is further mapped to lower-dimensional space, manifesting the holographic features of the dynamics. In particular, two fundamental time scales emerge in the dynamical evolution, with one mimicking the topological band on the momentum dimension and the other characterizing the residue time evolution of the state after the quench. For this, a universal duality between the quench dynamics and the equilibrium topological phase of the spin model is obtained in the time dimension by extracting information from the field evolution dynamics in modulated ring systems in simulations. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological nonequilibrium dynamics.
拓扑相的概念扩展到动力系统激发了广泛的研究，其中非平衡拓扑不变量的表征是核心问题，通常需要时间和动量维度上的量子动力学信息。在此，我们提出了合成维度中的拓扑全息猝灭动力学，并表明它提供了一种高效的方案来表征光子拓扑相。利用由光频率形成的合成晶格中的环形谐振器构建了一个赝自旋模型，通过初始化一个平凡态来诱导猝灭动力学，该平凡态在拓扑哈密顿量下演化。我们的关键预测是，哈密顿量的完整拓扑信息仅在时间维度上编码于猝灭动力学中，并进一步映射到低维空间，体现了动力学的全息特征。特别地，在动力学演化中出现了两个基本时间尺度，一个模拟动量维度上的拓扑能带，另一个表征猝灭后态的剩余时间演化。为此，通过在模拟中从调制环形系统中的场演化动力学提取信息，在时间维度上获得了猝灭动力学与自旋模型平衡拓扑相之间的普遍对偶性。这项工作还表明，光子合成频率维度为探索拓扑非平衡动力学提供了一种有效且强大的方法。
