We study an adiabatic topological passage of two Su-Schrieffer-Heeger (SSH) chains mediated by a nonlocal atom. When two finite SSH chains are in the topological phase and the frequency of the atom is equal to the center frequency of the SSH chains, the system is reduced to a subsystem that describes the coupling of a nonlocal atom to the edge states of two SSH chains. In this case, we can find dark states that act as adiabatic topological passages. This allows us to adiabatically transfer excitations of the atom to either end of two SSH chains in a fully controllable way. In addition, we show good robustness of the adiabatic topological passages to both atom frequency mismatch and the coupling disorders in the two SSH chains. Our study provides a method to realize quantum information processing and fabricate quantum optical devices based on the coupling of nonlocal atom to topological matter.

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• Quantum optics
• Quantum state transfer
• Su-Schrieffer-Heeger model