  We study theoretically potential advantages of two-component mixtures in
optical lattices with state-dependent tunneling for approaching
long-range-order phases and detecting easy-axis antiferromagnetic correlations.
While we do not find additional advantages of mixtures with large hopping
imbalance for approaching quantum magnetism in a harmonic trap, it is shown
that a nonzero difference in hopping amplitudes remains highly important for a
proper symmetry breaking in the pseudospin space for the single-site-resolution
imaging and can be advantageously used for a significant increase of the
signal-to-noise ratio and thus detecting long-range easy-axis antiferromagnetic
correlations in the corresponding experiments.
