Coherent State Description of the Ground State in the Tavis-Cummings Model and its Quantum Phase Transitions

TL;DR

This paper demonstrates that a tensorial product of coherent states effectively approximates the ground state and captures quantum phase transitions in the Tavis-Cummings model across different regimes.

Contribution

It introduces a coherent state-based approach that accurately models the ground state and quantum phase transitions in the Tavis-Cummings model for any number of atoms.

Findings

The trial state reproduces expectation values of observables accurately.

Agreement with exact solutions in field-matter entanglement and fidelity measures.

Analytic expressions for ground state observables are provided.

Abstract

Quantum phase transitions and observables of interest of the ground state in the Tavis-Cummings model are analyzed, for any number of atoms, by using a tensorial product of coherent states. It is found that this "trial" state constitutes a very good approximation to the exact quantum solution, in that it globally reproduces the expectation values of the matter and field observables. These include the population and dipole moments of the two-level atoms and the squeezing parameter. Agreement in the field-matter entanglement and in the fidelity measures, of interest in quantum information theory, is also found.The analysis is carried out in all three regions defined by the separatrix which gives rise to the quantum phase transitions. It is argued that this agreement is due to the gaussian structure of the probability distributions of the constant of motion and the number of photons. The expectation values of the ground state observables are given in analytic form, and the change of the ground state structure of the system when the separatrix is crossed is also studied.