  Exploring the properties and applications of topological quantum states is
essential to better understand topological matter. Here, we theoretically study
a quasi-one-dimensional topological atom array. In the low-energy regime, the
atom array is equivalent to a topological superatom. Driving the superatom in a
cavity, we study the interaction between light and topological quantum states.
We find that the edge states exhibit topology-protected quantum coherence,
which can be characterized from the photon transmission. This quantum coherence
helps us to find a superradiance-subradiance transition, and we also study its
finite-size scaling behavior. The superradiance-subradiance transition also
exists in symmetry-breaking systems. More importantly, it is shown that the
quantum coherence of the subradiant edge state is robust to random noises,
allowing the superatom to work as a topologically protected quantum memory. We
suggest a relevant experiment with three-dimensional circuit QED. Our study may
have applications in quantum computation and quantum optics based on
topological edge states.
