The Critical Point Entanglement and Chaos in the Dicke Model

Entropy

Lina Bao²  Feng Pan²  Jing Lu²  Jerry P. Draayer³  Demosthenes Ellinas¹  Giorgio Kaniadakis¹  Jiannis Pachos¹ 

[1] Department of Physics, Liaoning Normal University, Dalian 116029, China;;Department of Physics, Liaoning Normal University, Dalian 116029, China; E-Mails:;Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA; E-Mail:

关键词: entanglement;    quantum phase transition;    level statistics;    quantum chaos;   

DOI  :  10.3390/e17075022

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland