Geometry, quantum correlations, and phase transitions in the $\Lambda$-atomic configuration

TL;DR

This paper investigates the quantum phase diagram of a three-level $ ext{Lambda}$-configuration atom interacting with a two-mode field, using information measures and geometric representations to analyze phase transitions, symmetry breaking, and entanglement.

Contribution

It introduces a combined approach using fidelity, entanglement, and geometric simplex representation to analyze quantum phases and symmetry breaking in a $ ext{Lambda}$-system.

Findings

Quantum phases are characterized by spontaneous symmetry breaking.

A geometric simplex representation visualizes entanglement and purity.

Comparison between variational states and numerical diagonalization reveals differences in entanglement.

Abstract

The quantum phase diagram for a finite $3$-level system in the $\Lambda$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility and entanglement, applied to the reduced density matrix of the matter sector of the system. The quantum phases are explained by emphasizing the spontaneous symmetry breaking along the separatrix. Additionally, a description of the reduced density matrix of one atom in terms of a simplex allows a geometric representation of the entanglement and purity properties of the system. These concepts are calculated for both, the symmetry-adapted variational coherent states and the numerical diagonalisation of the Hamiltonian, and compared. The differences in purity and entanglement obtained in both calculations can be explained and visualised by means of this simplex representation.