The observation of the rare neutrinoless-double-beta-decay will have major implications for both neutrino physics and particle physics as a whole. In particular, a positive observation will conrm the Majorana nature of the neutrino and demonstrate that lepton number is not a strictly conserved quantity. Furthermore, a measurement of the half-life of the decay will lend itself to a measurement of the absolute mass scale of the neutrino. In this work, the sensitivity to observing the neutrinoless-double-beta-decay of 136 Xe is analyzed for the EXO experiment, and the benets of the inclusion of a barium-tagging system in a future tonne-scale detector are demonstrated. In addition, the sensitivity to single barium ion identication is analyzed for two dierent methods of observation: continuous excitation and intermodulation. The intermodulation technique was determined to be the more sensitive as single barium ions were observed with a relatively high signal-to-noise ratio of ∼4 for a one second observation time. Single ions were not observed using the continuous excitation technique.