Controllable operations of edge states in cross-one-dimensional topological chains

Topological edge states have recently attracted intense interest due to their robustness in the presence of disorder and defects. However, most approaches for manipulating such states require global modulations of the system's Hamiltonian. In this work, we develop a method to control edge states using local interactions of a four-node junction between cross-one-dimensional topological atomic chains. These junction interactions can give rise to tunable couplings between the hybridized edge states within different geometric symmetries, allowing us to implement robust quantum state transfer and gate between the two topological chains via a double-quench protocol. Moreover, when the atoms in chains are precisely positioned and coupled to waveguides, the correlated decay caused by the environment enables the symmetric edge states to present subradiant dynamics and thus show extremely long coherence time. These findings open up possibilities for future quantum technologies with topological edge states.