Quantum Tomography of a system of three-level atoms

TL;DR

This paper investigates the feasibility of quantum state tomography for three-level atomic systems, identifying conditions under which complete or partial reconstruction is possible in different configurations.

Contribution

It provides a detailed analysis of quantum tomography possibilities for three-level atoms, highlighting the impact of degeneracy and atomic configuration on reconstructability.

Findings

Complete tomography is possible for non-degenerate three-level atoms.

Partial reconstruction is limited to certain configurations in degenerate cases.

Explicit examples for one and two-atom systems illustrate the theoretical results.

Abstract

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.