  In the study of relaxation processes in coherent non-equilibrium dynamics of
quenched quantum systems, ultracold atoms in optical superlattices with
periodicity two provide a very fruitful test ground. In this work, we consider
the dynamics of a particular, experimentally accessible initial state prepared
in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the
entire range of interaction strengths, further investigating the issues raised
in Ref. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation
dynamics analytically in the non interacting and hard core bosonic limits,
deriving explicit expressions for the dynamics of certain correlation
functions, and numerically for finite interaction strengths using the
time-dependent density-matrix renormalization (t-DMRG) approach. We can
identify signatures of local relaxation that can be accessed experimentally
with present technology. While the global system preserves the information
about the initial condition, locally the system relaxes to the state having
maximum entropy respecting the constraints of the initial condition. For finite
interaction strengths and finite times, the relaxation dynamics contains
signatures of the relaxation dynamics of both the non-interacting and hard core
bosonic limits.
