Ultra-cold atoms in optical lattices have been exploited to study the Mott-insulator transition in 1, 2, and 3 dimensions; here we focus on the 2D Mott-insulator transition. Initially Bose-condensed rubidium atoms are loaded into a 3D optical lattice with an average occupancy of one atom per-site. By making the lattice much deeper in one direction than the remaining two, we construct an ensemble of 2D lattice systems. These 2D systems exhibit a superfluid-insulator transition as the lattice depth is increased. We present new measurements that show that the conventional signature of long-range order, namely diffraction, disappears continuously as the Mott state develops, and we extract the remnant coherence length from the width of these structures peaks. |