We present an in-situ study of an optical lattice with tunneling and single lattice site resolution. This system provides an important step for realizing a quantum computer. The real-space images show the fluctuations of the atom number in each site. The sub-Poissonian distribution results from the approach to the Mott insulator state, combined with the dynamics of density-dependent losses, which result from the high densities of optical lattice experiments. These losses are clear from the shape of the lattice profile. Furthermore, we find that the lattice is not in the ground state despite the momentum distribution which shows the reciprocal lattice. These effects may well be relevant for other optical lattice experiments, past and future. The lattice beams are derived from a microlens array, resulting in lattice beams which are perfectly stable relative to one another.
