Entangled States and Super-radiant Phase Transition

TL;DR

This paper analyzes the thermodynamics and phase transitions of the Dicke model with dipole-dipole interactions, showing that entanglement influences the super-radiant transition without altering its critical behavior.

Contribution

It introduces dipole-dipole interactions into the Dicke model and studies their effect on phase transitions and entanglement, revealing the robustness of critical behavior.

Findings

Dipole-dipole interactions do not modify the critical behavior of the phase transition.

Entangled states are generated in the atomic system due to dipole-dipole interactions.

The transition from fluorescent to super-radiant phase is characterized and analyzed.

Abstract

The Dicke spin-boson model is composed by a single bosonic mode and an ensemble of $N$ identical two-level atoms. Assuming thermal equilibrium with a reservoir at temperature $\beta^{-1}$, we consider the situation where the coupling between the bosonic mode and the atoms generates resonant and non-resonant processes. The thermodynamic of the model is investigated. Next we introduce dipole-dipole interaction between the atoms. We investigate the transition from fluorescent to super-radiant phase and the quantum phase transition in a situation where the dipole-dipole interaction between the atoms generates entangled states in the atomic system. We proved that, the critical behavior is not modified by the introduction of the dipole-dipole interaction.