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

TL;DR

This paper investigates the phase diagram and entanglement properties of a three-level Dicke model by analyzing the Wigner function and fidelity criteria, revealing regions of non-classical states and phase transitions.

Contribution

It introduces a detailed analysis of the ground state and phase transitions of a three-level Dicke model using Wigner functions and Bures distance, providing new insights into quantum entanglement.

Findings

Identification of regions with Wigner function negativity indicating non-classical states

Mapping of entanglement regions within the phase diagram

Finer classification of phase transitions via Bures distance surface

Abstract

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.