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Quantum Phase Transition and Entanglement in the Detuned Dicke Model

Ru-Fen Liu, Chia-Chu Chen

Published Oct 11, 2005• 0 citations
OpenAlex

Abstract

The quantum phase transition of mono-mode Dicke models with two atoms is discussed and analytical results are presented. For arbitrary detuning, the exact spectrum and the concurrence of entanglement are calculated for the two-atoms system. It is shown that sequential quantum phase transitions occur in this system. Evidences have been found to support that quantum phase transition and concurrence are uncorrelated in this particular model. Furthermore, the results of quantum phase transition with extra mode are also discussed.

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The quantum phase transition of mono-mode Dicke models with two atoms is discussed and analytical results are presented. For arbitrary detuning, the exact spectrum and the concurrence of entanglement are calculated for the two-atoms system. It is shown that sequential quantum phase transitions occur in this system. Evidences have been found to support that quantum phase transition and concurrence are uncorrelated in this particular model. Furthermore, the results of quantum phase transition with extra mode are also discussed.
The dipole-coupled two-level atoms (qubits) in a single-mode resonant cavity are studied by extended bosonic coherent states. The numerical solution is presented. The first-order quantum phase transitions may occur in finite systems, in contrast to the original Dicke model. This system also exhibits a second-order quantum phase transition from the normal to the superradiant phase, as in the original Dicke model. Finite-size scaling for several observables---such as average fidelity susceptibility, order parameter, and concurrence---is performed for different interatomic interactions. The scaling exponents obtained suggest that interatomic interactions do not change the universality class.
Quantum many-body systems that support high-order quantum phase transitions are quite rare. Here we consider an important generalization of the Dicke model in which an ensemble of multilevel atoms, instead of two-level atoms as in the conventional Dicke model, interact with a single photonic mode, and show that this generalized Dicke model can become multicritical. For a subclass of experimentally realizable schemes, multicritical conditions of arbitrary order can be expressed analytically in compact forms. As such, experiments can be readily designed to achieve quantum phase transition of desired order. We also calculate the atom-photon entanglement entropy for both critical and noncritical cases and find that the order of the criticality strongly affects the critical entanglement entropy: higher order yields stronger entanglement. Our work provides deep insight into quantum phase transitions and multicriticality.
We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N --> infinity limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition. Our considerations of the wave function indicate that this is connected with a delocalization of the system and the emergence of macroscopic coherence. We also derive a semiclassical Dicke model that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.
The full Dicke model is composed of a single bosonic mode and an ensemble of NNN identical two-level atoms. In the model, the coupling between the bosonic mode and the atoms generates resonant and nonresonant processes. We also consider a dipole-dipole interaction between the atoms, which is able to generate entangled states in the atomic system. By assuming thermal equilibrium with a reservoir at temperature ${\ensuremath{\beta}}^{\ensuremath{-}1}$, the transition from fluorescent to superradiant phase and the quantum phase transition are investigated. It is shown that the critical behavior of the full Dicke model is not modified by the introduction of the dipole-dipole interaction.
The Dicke model generalized to the case where the dependence of the coupling constant on individual atoms is taken into account is investigated. It is shown that the generalized Dicke model exhibits a quantum phase transition from the normal phase to the superradiant phase in the thermodynamic limit, as well as the standard Dicke model. The mean photon number, the atomic inversion, the lowest excitation energy, and the entanglement entropy between the field and the atoms are evaluated analytically or numerically, and the critical behavior is examined. As a result, it turns out that the critical behavior in the generalized model is essentially the same as that in the standard model. This implies universality in the Dicke model.