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.