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The usual Su-Schrieffer-Heeger model with an even number of lattice sitespossesses two degenerate zero energy modes. The degeneracy of the zero energymodes leads to the mixing between the topological left and right edge states,which makes it difficult to implement the state transfer via topological edgechannel. Here, enlightened by the Rice-Male topological pumping, we find thatthe staggered periodic next-nearest neighbor hoppings can also separate theinitial mixed edge states, which ensures the state transfer between topologicalleft and right edge states. Significantly, we construct an unique topologicalstate transfer channel by introducing the staggered periodic on-site potentialsand the periodic next-nearest neighbor hoppings added only on the odd sitessimultaneously, and find that the state initially prepared at the last site canbe transfered to the first two sites with the same probability distribution.This special topological state transfer channel is expected to realize atopological beam splitter, whose function is to make the initial photon at oneposition appear at two different positions with the same probability. Further,we demonstrate the feasibility of implementing the topological beam splitterbased on the circuit quantum electrodynamic lattice. Our scheme opens up a newway for the realization of topological quantum information processing andprovides a new path towards the engineering of new type of quantum opticaldevice.

Engineering of topological state transfer and topological beam splitter in an even-size Su-Schrieffer-Heeger chain