  Ultra-cold atoms in optical lattices provide an ideal platform for exploring
many-body physics of a large system arising from the coupling among a series of
small identical systems whose few-body dynamics is exactly solvable. Using
Landau-Zener (LZ) transition of bosonic atoms in double well optical lattices
as an experimentally realizable model, we investigate such few to many body
route by exploring the relation and difference between the small few-body (in
one double well) and the large many-body (in double well lattice)
non-equilibrium dynamics of cold atoms in optical lattices. We find the
many-body coupling between double wells greatly enhances the LZ transition
probability. The many-body dynamics in the double well lattice shares both
similarity and difference from the few-body dynamics in one and two double
wells. The sign of the on-site interaction plays a significant role on the
many-body LZ transition. Various experimental signatures of the many-body LZ
transition, including atom density, momentum distribution, and density-density
correlation, are obtained.
