Studies of atomic motion and atomic diagnostics in optical lattices

We present a detailed theoretical and numerical study of polarization gradient cooling for alkali atoms with large ground state angular momenta (F_g ≥ 2) moving in a one dimensional (1D) lin⊥lin optical lattice in order to clarify the physical picture of laser cooling in steady-state. Using a basis of Wannier states we find that the semiclassical picture of laser cooling depends strongly on coherences between the Zeeman sublevels of the atomic ground state. We find that atoms with ground state angular momenta F_g = 2, tend to diffuse throughout the lattice, while atoms with higher ground state angular momentum tend to remain localized at specific lattice sites.; In the far-off resonance case, the lattice is essentially dissipation free allowing for studies of quantum-state control. We examine the creation and manipulation of mesoscopic coherent superpositions of Cesium atoms in magneto-optical double-potential wells created by a far-off-resonance 1D lin-&thetas;-lin lattice. A robust set of dynamically varied lattice parameters that lead to a tunneling situation. Tunneling oscillations computed numerically agree with experiment except for an observed decay in tunneling oscillations.; We consider the addition of a time-periodic drive to the double-well system, for which certain parameters of the drive, it is possible to coherently suppress tunneling. When a small amount of noise is added to the system in the form of random periodic δ-function “kicks” the quantum interference is destroyed. However, increasing the strength of the noise appears to have a stabilizing effect on the coherent suppression of tunneling.; High resolution spatial information about atomic samples trapped in optical lattices can be obtained directly without the use of external probe lasers which necessarily disturb the system and whose resolution is limited by the wavelength of the probe laser. We explore the use of first and second order same-time atomic spatial correlation functions as a diagnostic for probing the small scale spatial structure of atomic samples trapped in optical lattices. Assuming an ensemble of equivalent atoms, properties of the local wave function at a given lattice site can be measured using same-position first-order correlations. Statistics of atomic distributions over the lattice can be measured via two-point correlations. (Abstract shortened by UMI.)...