Phase space tomography of classical and nonclassical vibrational states of atoms in an optical lattice

Atoms trapped in an optical lattice have long been a system of interest in the atomic, molecular and optical community, and in recent years much study has been devoted to both short- and long-range coherence in this system, as well as to its possible applications to quantum information processing. Here we demonstrate for the first time a complete determination of the quantum phase space distributions for an ensemble of 85Rb atoms in such a lattice, including a negative Wigner function for atoms in an inverted state.