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In this paper, we study the interaction between atom and the finite-sizeSu-Schrieffer-Heeger (SSH) model. We find that when the finite SSH model in thetrivial phase, it can be viewed as the atom coupling with the waveguide withthe finite bandwidths and non-linear dispersion relation. However, for the SSHmodel in the topological phase, when we consider the frequency of the atom isresonant with the edge mode of the SSH model, we find that the atom statecouples to the two edge states. In this case, we find that there exists aspecial channel that can be utilized to transfer the atomic excitation to theends of the SSH model using adiabatic processes. When the atom couples to thedifferent sub-lattice, the excitation of the atom can be transferred to theleftmost or rightmost end of the chain, which provides the potentialapplication toward quantum information processing. Furthermore, The excitationtransfer of excited states of atoms to the ends of the chain can also berealized without the adiabatic process. Our work provides a pathway forrealizing controllable quantum information transfer based on the atom couplestopological matter.

Realizing the controllable excitation transfer based on the atom coupling the finite-size Su-Schrieffer-Heeger model