  Ultracold atoms in optical lattices are a versatile tool to investigate
fundamental properties of quantum many body systems. In particular, the high
degree of control of experimental parameters has allowed the study of many
interesting phenomena such as quantum phase transitions and quantum spin
dynamics. Here we demonstrate how such control can be extended down to the most
fundamental level of a single spin at a specific site of an optical lattice.
Using a tightly focussed laser beam together with a microwave field, we were
able to flip the spin of individual atoms in a Mott insulator with
sub-diffraction-limited resolution, well below the lattice spacing. The Mott
insulator provided us with a large two-dimensional array of perfectly arranged
atoms, in which we created arbitrary spin patterns by sequentially addressing
selected lattice sites after freezing out the atom distribution. We directly
monitored the tunnelling quantum dynamics of single atoms in the lattice
prepared along a single line and observed that our addressing scheme leaves the
atoms in the motional ground state. Our results open the path to a wide range
of novel applications from quantum dynamics of spin impurities, entropy
transport, implementation of novel cooling schemes, and engineering of quantum
many-body phases to quantum information processing.
