Simulation of topological quantum state transfer in a two-dimensional waveguide model

Topological pumping is a quantum state transfer phenomena in topological systems, which was studied in one-dimensional and two-dimensional topological systems and is highly valuable in the generation of entangled states by adiabatic management. In this study, we develop a robust, rapid quantum state transfer mechanism based on Su-Schrieffer-Heeger (SSH) chains. This mechanism considers the case where the propagation length determines the interchain coupling. We concentrate on the selection of different slowly varying functions, which is critical for optimizing the quantum pumping. Based on the coupled mode theory, we study the zero-energy state spatial transfer in a one-dimensional SSH chain waveguide and a two-dimensional rhombic lattice waveguide model, extending the zero-energy state transfer from edge to edge to corner to corner. To obtain optical transport with faster transfer speed, higher fidelity, and topological protection, we optimize the tangent function and the length of the optical waveguide so that the zero-energy eigenstates evolve adiabatically following the topological boundary state without exciting other levels. The findings of this work will open up possibilities for the construction of reliable quantum state transfer channels and hold significant promise for information processing and optical manipulation.