Chaos and the quantum phase transition in the Dicke model

Clive Emary and Tobias Brandes
Phys. Rev. E 67, 066203 – Published 12 June 2003
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Abstract

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 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.

  • Received 15 January 2003

DOI:https://doi.org/10.1103/PhysRevE.67.066203

©2003 American Physical Society

Authors & Affiliations

Clive Emary* and Tobias Brandes

  • Department of Physics, UMIST, P.O. Box 88, Manchester M60 1QD, United Kingdom

  • *Email address: emary@theory.phy.umist.ac.uk

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Vol. 67, Iss. 6 — June 2003

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