  We numerically investigate, using the time evolving block decimation
algorithm, the quantum transport of ultra-cold bosonic atoms in a double well
optical lattice through slow and periodic modulation of the lattice parameters
(intra- and inter-well tunneling, chemical potential, etc.). The transport of
atoms does not depend on the rate of change of the parameters (as along as the
change is slow) and can distribute atoms in optical lattices at the quantized
level without involving external forces. The transport of atoms depends on the
atom filling in each double well and the interaction between atoms. In the
strongly interacting region, the bosonic atoms share the same transport
properties as non-interacting fermions with quantized transport at the half
filling and no atom transport at the integer filling. In the weakly interacting
region, the number of the transported atoms is proportional to the atom
filling. We show the signature of the quantum transport from the momentum
distribution of atoms that can measured in the time of flight image. A
semiclassical transport model is developed to explain the numerically observed
transport of bosonic atoms in the non-interacting and strongly interacting
limits. The scheme may serve as an quantized battery for atomtronics
applications.
