Phase Space Tomography of Classical and Nonclassical Vibrational States of Atoms in an Optical Lattice

Atoms trapped in optical lattice have long been a system of interest in the AMO 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 complete determination of the quantum phase space distributions for an ensemble of $^{85}Rb$ atoms in such a lattice, including a negative Wigner function for atoms in an inverted state.