Symmetry Adapted Coherent States for Three-Level Atoms Interacting with One-Mode Radiation

TL;DR

This paper develops symmetry-adapted coherent states as variational tools to analytically study the ground and excited states of three-level atoms interacting with a quantized field, revealing quantum phase transitions and entanglement properties.

Contribution

It introduces a novel analytical approach using symmetry-preserving coherent states for three-level atom-field systems, providing explicit expressions for quantum states and phase diagrams.

Findings

Analytical expressions for ground and excited states.

Identification of quantum phase transitions.

Quantification of atom-field entanglement.

Abstract

We introduce a combination of coherent states as variational test functions for the atomic and radiation sectors to describe a system of Na three- level atoms interacting with a one-mode quantised electromagnetic field, with and without the rotating wave approximation, which preserves the symmetry presented by the Hamiltonian. These provide us with the possibility of finding analytical solutions for the ground and first excited states. We study the properties of these solutions for the V-configuration in the double resonance condition, and calculate the expectation values of the number of photons, the atomic populations, the total number of excitations, and their corresponding fluctuations. We also calculate the photon number distribution and the linear entropy of the reduced density matrix to estimate the entanglement between matter and radiation. For the first time, we exhibit analytical expressions for all of these quantities, as well as an analytical description for the phase diagram in parameter space, which distinguishes the normal and collective regions, and which gives us all the quantum phase transitions of the ground state from one region to the other as we vary the interaction parameters (the matter-field coupling constants) of the model, in functional form.