Investigating the quench dynamics of the bound states in a spin-orbital-coupling system using a trapped ion

The quantum walk, as the quantum analog of the classical random walk, provides a feasible platform to study the topological phenomenon and nonequilibrium dynamics. Here we propose a scheme to realize the quantum walk with a single trapped ion where the Fock states provides the walk space and the zero-phonon state $|n=0\ensuremath{\rangle}$ serves as its natural boundary. Thus, our scheme offers an opportunity to investigate the dynamics of the bound states of the corresponding topological systems. In particular, the quench dynamics of the bound states can be extensively studied by tuning the bulk parameters and the local boundary operator, which are experimentally accessible. Our proposal not only offers an alternative approach to exploring the character of the bound states of the topological systems, but also offers a way to determine different phases through the dynamical processes.