Quantum Tunneling-induced Hybridization and Coherent Dynamics of Jackiw-Rebbi Zero Modes in a Modified Su-Schrieffer-Heeger Chain

Abstract

We investigate analytically and numerically the tunneling-induced hybridization and coherent dynamics of Jackiw-Rebbi (JR) zero modes in a modified Su-Schrieffer-Heeger (SSH) model. Unlike the conventional SSH model, this modified system possess two bulk gap closing points, namely, the quadratic-type gap closing point at $k=0$ and the Dirac-type gap closing point at $k=\pmπ/4a$. While the quadratic point does not support a topological domain wall due to the absence of mass inversion, the low-energy Dirac theory around $k=\pmπ/4a$ predicts an effective mass that changes sign at two spatially separated interfaces under a kink profile, generating a pair of JR bound states localized at those interfaces. We show that finite overlap between the JR zero modes lifts the zero-energy degeneracy through quantum tunneling, producing symmetric-antisymmetric hybridized states analogous to a quantum mechanical double-well system. An effective two-level description reveals coherent oscillations of the occupation probability between the two JR modes, accompanied by periodic transfer of sublattice polarization between the (A,C) and (B,D) sectors. The oscillation period is governed by the hybridization gap, providing a tunable route for controlling topological bound states. Our results establish a unified framework connecting JR zero modes, quantum tunneling, and coherent dynamics in modified SSH systems, offering a promising platform for controllable topological quantum-state transfer in engineered lattice structures.