Probing the Superfluid to Mott Insulator Transition at the Single Atom Level

Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We investigate the Bose-Hubbard model on a microscopic level using single atom-single lattice site imaging; our technique enables space- and time-resolved characterization of the number statistics across the superfluid-Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition timescales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low entropy phases in a lattice.