In the past decades, the discovery of the topological quantum phase has revolutionized the understanding of the fundamental phases of quantum matter. The classification of the topological quantum phase usually based on the equilibrium state. Non-equilibrium topological dynamics based on quench dynamics had been proposed to characterize the exotic behaviors beyond the equilibrium state. However, the characterization of non-equilibrium topological invariants typically needs the information of quantum dynamics in both the time and spatial dimension.

Therefore, the research team proposed the holographic quench dynamics by utilizing the concept of synthetic frequency dimension. The combination of the quench dynamics and the synthetic frequency dimension effectively facilitates the detection of topological invariants by using the information solely along the time dimension. The research potentially points towards the convenience and practicability of non-equilibrium state detection in future experiments. This result is in sharp contrast to the previous characterization of equilibrium topological phases through the nonequilibrium topological invariants, which necessitates the information in both the time dimension and momentum space, and hence leads to significant simplification for performing dynamical characterization of topological quantum phases in different synthetic models.

Fig. The dynamical spin texture that exhibits the topological winding feature.

The research was published in“Danying Yu, Bo Peng, Xianfeng Chen, Xiong-Jun Liu, and Luqi Yuan, Topological holographic quench dynamics in a synthetic frequency dimension, Light: Science & Applications 10, 209 (2021)”

Link：https://www.nature.com/articles/s41377-021-00646-y