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arXiv:quant-ph/0503195 · Physical Review Letters

Instability and Entanglement of the Ground State of the Dicke Model

Vladimír Bužek, Miguel Orszag, Marián Roško

Published Apr 26, 2005• 78 citations
arXivHTMLPDF

Abstract

Using tools of quantum information theory we show that the ground state of the Dicke model exhibits an infinite sequence of instabilities (quantum-phase-like transitions). These transitions are characterized by abrupt changes of the bi-partite entanglement between atoms at critical values kappa(j) of the atom-field coupling parameter kappa and are accompanied by discontinuities of the first derivative of the energy of the ground state. We show that in a weak-coupling limit (kappa1 < or = kappa < or = kappa2) the Coffman-Kundu-Wootters inequalities are saturated, which proves that for these values of the coupling no intrinsic multipartite entanglement (neither among the atoms nor between the atoms and the field) is generated by the atom-field interaction. We show that in the strong-coupling limit the entangling interaction with atoms leads to a highly sub-Poissonian photon statistics of the field mode.

DOI
10.1103/physrevlett.94.163601

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Using tools of quantum information theory we show that the ground state of the Dicke model exhibits an infinite sequence of instabilities (quantum-phase-like transitions). These transitions are characterized by abrupt changes of the bi-partite entanglement between atoms at critical values kappa(j) of the atom-field coupling parameter kappa and are accompanied by discontinuities of the first derivative of the energy of the ground state. We show that in a weak-coupling limit (kappa1 < or = kappa < or = kappa2) the Coffman-Kundu-Wootters inequalities are saturated, which proves that for these values of the coupling no intrinsic multipartite entanglement (neither among the atoms nor between the atoms and the field) is generated by the atom-field interaction. We show that in the strong-coupling limit the entangling interaction with atoms leads to a highly sub-Poissonian photon statistics of the field mode.
Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS). Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.
We investigate the entanglement properties of an ensemble of atoms interacting with a single bosonic field mode via the Dicke (superradiance) Hamiltonian. The model exhibits a quantum phase transition and a well-understood thermodynamic limit, allowing the identification of both quantum and semi-classical many-body features in the behavior of the entanglement. We consider entanglement between the atoms and field, as well both bi- and multi- partite entanglement between atoms. In the thermodynamic limit, we give exact results for all entanglement partitions and observe a logarithmic divergence of the atom-field entanglement, and discontinuities in the pairwise and multipartite entanglement.
We consider a set of two level atoms interacting with a single quantized bosonic mode governed by the Dicke model. In this model it is well known that under a critical value of the light-matter coupling a spontaneous radiation process takes place. In the present work, we investigate the dynamics of the system and we study the Wigner distribution function to visualize the effect of the minimal coupling on the ground state wavefunction from the normal phase to the superradiant one. We show also that the entanglement of Bi-partite model is limited by the presence of the diamagnetic term.
We show how various mathematical formalisms, specifically the catastrophe formalism and group theory, aid in the study of relevant systems in quantum optics. We describe the phase transition of the Dicke model for a finite number N of atoms, via three different methods, which led to universal parametric curves for the expectation value of the first quadrature of the electromagnetic field and the expectation value of the number operator, as functions of the atomic relative population. These are valid for all values of the matter–field coupling parameter, and valid for both the ground and first-excited states. Using these mathematical tools, the critical value of the atom–field coupling parameter is found as a function of the number of atoms, from which its critical exponent is derived.
Abstract In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on the extended Dicke model’s ground state properties, the mean photon number, the scaled atomic population and the average ground energy are displayed. Using the self-consistent field theory to solve the atom-atom interaction, we discover the system undergoes a first-order quantum phase transition from the normal phase to the superradiant phase, but a famous Dicke-type second-order quantum phase transition without the atom-atom interaction. Meanwhile, the atom-atom interaction makes the phase transition point shift to the lower atom-photon collective coupling strength.
We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized electromagnetic field. The optical medium is pumped externally through a classical electric field, so that there is a degenerate parametric amplification effect, which strongly modifies the field dynamics without affecting the atomic sector. Through a semiclassical description the different phases of this extended Dicke model are described. The quantum phase transition is characterized with the expectation values of some observables of the system as well as the Berry phase and its first derivative, where such quantities serve as order parameters. It is remarkable that the model allows the control of the quantum criticality through a suitable choice of the parameters of the non-linear optical medium, which could make possible the use of a low intensity laser to access the superradiant region experimentally.