  We overcome the diffraction limit in fluorescence imaging of neutral atoms in
a sparsely filled one-dimensional optical lattice. At a periodicity of 433 nm,
we reliably infer the separation of two atoms down to nearest neighbors. We
observe light induced losses of atoms occupying the same lattice site, while
for atoms in adjacent lattice sites, no losses due to light induced
interactions occur. Our method points towards characterization of correlated
quantum states in optical lattice systems with filling factors of up to one
atom per lattice site.
