Quantum Tomography of a system of three-level atoms

We analyze the possibility of tomographic reconstruction of a system of three-level atoms in both non-degenerate and degenerate cases. In the non-degenerate case (when both transitions can be accessed independently) a complete reconstruction is possible. In the degenerate case (when both transitions are excited simultaneously) the complete reconstruction is achievable only for a single atom in the Sigma configuration. For multiple Sigma atoms, or even a single atom in the Lambda configuration, only partial reconstruction is possible. Examples of one and two-atom cases are explicitly considered.