Quantum Phase Diagrams of Matter-Field Hamiltonians II: Wigner Function Analysis

Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the three-level generalised Dicke model for a single atom and determine the structure of its phase diagram using a fidelity criterion. We also calculate the Wigner function of the electromagnetic modes of the ground state through the corresponding reduced density matrix, and show in the phase diagram the regions where entanglement is present. A finer classification for the continuous phase transitions is obtained through the computation of the surface of maximum Bures distance.