We study topological features of interacting spin-1 2 particles in one-dimensional state-dependent optical lattices. Due to the co-translational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound-states appear as a result of the non-trivial center-ofmass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center-of-mass can be described by a non-trivial center-of-mass Chern number.arXiv:1910.09948v1 [cond-mat.mes-hall] 22 Oct 2019

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We study hybrid atom-molecule quantum walks in one-dimensional optical lattices with two interacting bosonic atoms which may be converted into a molecule. The hybrid atom-molecule energy bands include a continuum band and two isolated bands, which respectively correspond to scattering states and dressed bound states (DBS's). Because of the atom-molecule coupling, the DBS's may appear even in the absence of atom-atom interaction. From an initial state of two atoms occupying the same site, in addition to independent quantum walks which correspond to scattering states, correlated quantum walks appear as a signature of DBS's. Even if the atom-atom interaction and the atom-molecule coupling are much stronger than the tunneling strengths, independent quantum walks may still appear under certain resonant conditions. The correlated quantum walks show two light-cones with different propagation velocities, which can be analytically explained by the effective tunneling strengths of the two different DBS's. Furthermore, the effective nearest-neighbor tunneling of DBS's can be suppressed to zero, which can be explained by the destructive interference between the atomic pair and the molecule. *