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Entropy 2015, 17(7), 5022-5042; doi:10.3390/e17075022

The Critical Point Entanglement and Chaos in the Dicke Model

1
Department of Physics, Liaoning Normal University, Dalian 116029, China
2
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Demosthenes Ellinas, Giorgio Kaniadakis, Jiannis Pachos and Antonio M. Scarfone
Received: 24 April 2015 / Revised: 28 June 2015 / Accepted: 14 July 2015 / Published: 16 July 2015
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
View Full-Text   |   Download PDF [3877 KB, uploaded 17 July 2015]   |  

Abstract

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. View Full-Text
Keywords: entanglement; quantum phase transition; level statistics; quantum chaos entanglement; quantum phase transition; level statistics; quantum chaos
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bao, L.; Pan, F.; Lu, J.; Draayer, J.P. The Critical Point Entanglement and Chaos in the Dicke Model. Entropy 2015, 17, 5022-5042.

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