Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 179-186).In this thesis, I present results from two Paul-trap based ion traps carried out in the Vuletić laboratory: the Atom-Ion trap for collision studies between cold atoms and cold ions, and the Cavity-Array trap for studying the interaction between ionic ensembles and photons. The Atom-Ion trap overlaps a surface-planar ion trap with a magneto-optical trap (MOT) for neutral atoms. The initial results of this system were loading of a shallow surface-planar ion trap at an unprecedented high rate of 4. 105 s-1 and isotopic purity by photoionization from the MOT. We demonstrate the first collisions between trapped atoms and trapped ions in the Langevin collision regime between Yb+ and Yb. A measurement of the Langevin rate constant through charge-exchange collisions between [alpha]Yb+ and [beta]Yb over three orders of magnitude in collision energy down to 3 yueV follows. The measured rate coefficient of 6 - 10-10 cm 3 s-1 is in good agreement with the Langevin model based on theoretical predictions of the polarizability of Yb. The theory and limits of sympathetic cooling of ions by localized cold atoms at low temperature is outlined. Measurements of momentum-transfer collisions between Yb+ and Rb are presented indicating that momentum-transfer collisions affect the ion energy at the Langevin rate. Finally, the fabrication and assembly of the Cavity-Array trap are presented. The Cavity-Array trap overlaps a high-finesse optical cavity with a linear array of Paul traps in order to reach the high co-operativity limit with trapped ions. Initial results from loading of the Cavity- Array trap are shown, indicating successful overlap of the optical cavity mode with the ion trapping region and the ability to load individual sites of the array ion trap.by Andrew T. Grier.Ph.D