Synthetic dimensions offer exciting new ways to explore higher-dimensional physics in lower geometrical dimensionality, simplify the setup for achieving unusual functionalities that are hard to be achieved in real space, and manipulate light in multiple ways.

Among them, dynamically modulated ring resonator systems, where resonant modes with equally spaced frequencies are coupled by external modulation to construct a synthetic frequency dimension, can provide great experimental flexibility and reconfigurability to construct more complex lattice structures.

Topological phases of matter play an essential role in many branches of photonics for providing exotic properties, which can be classified by their topological invariants.

For a one-dimensional (1D) system, such as the well-known SSH model, the topology is characterized by the Zak phase, which has been demonstrated within several experimental schemes in photonics. In spite of these progresses, there has been a remarkable challenge that the topological information of conventional 1D SSH model cannot be directly distinguished from the measured band structure in the current photonic or condensed matter platforms due to the identical band shapes for both topological trivial and non-trivial cases.