We describe an approach to the study of neutrino masses that combines quantum optics techniques with radiation detectors to obtain unprecedented sensitivity. With it the search for Majorana neutrino masses down to ∼10 meV will become accessible. The experimental technique uses the possibility of individually detecting Ba⁺-ions in the final state of ¹³⁶Xe double-beta decay via resonant excitation with a set of lasers aimed at a specific location in a large Time Projection Chamber. The specificity of the atomic levels provides tagging and, together with more traditional event recognition parameters, greatly suppresses radioactive backgrounds.