Application of precision laser spectroscopy and optical clock technology to the ground and metastable, first excited state of the ²²⁹Th nucleus at < 10 eV has significant potential for use in optical frequency metrology and tests of variation of fundamental constants. This work is a report on the development of required technologies to realize such a nuclear optical clock with a single, trapped, laser cooled ²²⁹Th³⁺ ion. Creation, trapping, laser cooling, and precision spectroscopy are developed and refined first with the naturally occurring isotope, ²³²Th. These technologies are then extended to laser cooling and precision laser spectroscopy of the electronic structure of ²²⁹Th³⁺. An efficient optical excitation search protocol to directly observe this transition via the electron bridge is proposed. The extraordinarily small systematic clock shifts are estimated and the likely extraordinarily large sensitivity of the clock to variation of the fine structure constant is discussed.

This thesis presents the investigations of Rubidium atoms in magneto-optical traps and triply charged Thorium ions in electrodynamic traps for future advances in long-distance quantum telecommunication, next generation clocks, and fundamental tests of current physical theories. Experimental realizations of two core building blocks of a quantum repeater are described: a multiplexed quantum memory and a telecom interface for long-lived quantum memories. A color change of single-photon level light fields by several hundred nanometers in an optically thick cold gas is demonstrated, while preserving quantum entanglement with a remotely stored matter excitation. These are essential elements for long-distance quantum telecommunication, fundamental tests of quantum mechanics, and applications in secure communication and computation. The first trapping and laser cooling of Thorium-229 ions are described. Thorium-229 nuclear electric quadrupole moment is revealed by hyperfine spectroscopy of triply charged Thorium-229 ions. A system to search for the isomer nuclear transition in Thorium-229 is developed and tested with the excitation of a forbidden electronic transition at 717 nm. Direct excitation of the nuclear transition with laser light would allow for an extremely accurate clock and a sensitive test bed for variations of fundamental physical constants, including the fine structure constant.