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