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arXiv:0901.2705 · Optics Communications

Instabilities of the Dicke model with field interactions

Yuyu Zhang, Tao Liu, Qing‐Hu Chen, Kelin Wang

Published May 20, 2010• 2 citations
arXivHTMLPDF
DOI
10.1016/j.optcom.2010.04.097

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The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes.
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.
We study composite quantum systems, like the Dicke model (or the generalized quantum Rabi model), in the absence of external driving by resorting to methods from quantum field theory.It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution.To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for a vacuum survival probability of the dissipative system.In the ultra-strong coupling regime, we show that the timedependent coherent state generated by an interaction Hamiltonian behaves non-unitary irreversible time evolution.