  In Pedersen et al. (2011) we proposed a method to utilize a temporally
dependent superlattice potential to mediate spin-selective transport, and
thereby probe long and short range magnetic correlations in optical lattices.
Specifically this can be used for detecting antiferromagnetic ordering in
repulsive fermionic optical lattice systems, but more generally it can serve as
a means of directly probing correlations among the atoms by measuring the mean
value of an observable, the number of double occupied sites. Here, we provide a
detailed investigation of the physical processes which limit the effectiveness
of this "conveyer belt method". Furthermore we propose a simple ways to improve
the procedure, resulting in an essentially perfect (error-free) probing of the
magnetic correlations. These results shows that suitably constructed
superlattices constitute a promising way of manipulating atoms of different
spin species as well as probing their interactions.
