Topological flat band with higher winding number in a superradiance lattice

A five-level M-type scheme in atomic ensembles is proposed to generate a one-dimensional bipartite superradiance lattice in momentum space. By taking advantage of this tunable atomic system, we show that various types of Su-Schrieffer-Heeger (SSH) model, including the standard SSH and extended SSH model, can be realized. Interestingly, it is shown that through changing the Rabi frequencies and detunings in our proposed scheme, there is a topological phase transition from topological trivial regime with winding number being 0 to topological non-trivial regime with winding number being 2. Furthermore, a robust flat band with higher winding number (being 2) can be achieved in the above topological non-trivial regime, where the superradiance spectra can be utilized as a tool for experimental detection. Our proposal would provide a promising approach to explore new physics, such as fractional topological phases, in the flat bands with higher topological number.