Hybrid atom-molecule quantum walks in one-dimensional optical lattice

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.