Engineering the topological state transfer and topological beam splitter in an even-sized Su-Schrieffer-Heeger chain

The usual Su-Schrieffer-Heeger model with an even number of lattice sites possesses two degenerate zero-energy modes. The degeneracy of the zero-energy modes leads to the mixing between the topological left- A nd right-edge states, which makes it difficult to implement the state transfer via topological edge channel. Here, enlightened by the Rice-Male topological pumping, we find that the staggered periodic next-nearest-neighbor hoppings can also separate the initial mixed edge states, which ensures the state transfer between topological left- A nd right-edge states. Significantly, we construct a unique topological state transfer channel by introducing the staggered periodic onsite potentials and the periodic next-nearest-neighbor hoppings added only on the odd sites simultaneously, and we find that the state initially prepared at the last site can be transferred to the first two sites with the same probability distribution. This special topological state transfer channel is expected to realize a topological beam splitter, whose function is to make the initial photon at one position appear at two different positions with the same probability. Further, we demonstrate the feasibility of implementing the topological beam splitter based on the circuit quantum electrodynamic lattice. Our scheme opens up a new way for the realization of topological quantum information processing and provides a path toward the engineering of new type of quantum optical device.