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Physical Review A

Decoherence, entanglement, and chaos in the Dicke model

Xi-Wen Hou, Bambi Hu

Published Apr 23, 2004• 66 citations
Publisher

Abstract

The dynamical properties of quantum entanglement in the Dicke model without rotating-wave approximation are investigated in terms of the reduced-density linear entropy. The characteristic time of decoherence process in the early-time evolution is numerically obtained and it is shown that the characteristic time decreases as the coupling parameter increases. The mean entanglement, which is defined to be averaged over time, is employed to describe the influences of both quantum phase transition and corresponding classical chaos on the behavior of entanglement. For a given energy, initial conditions are taken to be minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. It is shown that the entanglement has a distinct change at the quantum phase transition, and that the entanglement for regular initial conditions is smaller than that for chaotic ones in the case of weak coupling, while it fluctuates with small amplitude in strong coupling and for chaotic initial conditions.

DOI
10.1103/physreva.69.042110

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The dynamical properties of quantum entanglement in the Dicke model without rotating-wave approximation are investigated in terms of the reduced-density linear entropy. The characteristic time of decoherence process in the early-time evolution is numerically obtained and it is shown that the characteristic time decreases as the coupling parameter increases. The mean entanglement, which is defined to be averaged over time, is employed to describe the influences of both quantum phase transition and corresponding classical chaos on the behavior of entanglement. For a given energy, initial conditions are taken to be minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. It is shown that the entanglement has a distinct change at the quantum phase transition, and that the entanglement for regular initial conditions is smaller than that for chaotic ones in the case of weak coupling, while it fluctuates with small amplitude in strong coupling and for chaotic initial conditions.
Manifestation of chaotic behavior is found in an intrinsically quantum property. The entanglement process, quantitatively expressed in terms of the reduced density linear entropy, is studied for the NNN-atom Jaynes-Cummings model. For a given energy, initial conditions are prepared as minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. We find for short times a faster increase in decoherence for the chaotic initial conditions as compared to regular ones, which have oscillatory increase.
The Dicke model displays quantum chaotic dynamic properties in the without-rotating-wave approximation. We explore the dynamic properties of the single-particle coherence in Dicke model by using the first-order temporal correlation function and numerical simulation. The results reveal that the first-order temporal correlation function decays very rapidly when the initial coherent state is centered in chaotic regions, but rather slowly when the initial coherent state is centered in regular regions. This indicates that the single-particle coherence is highly sensitive to initial states, and the classical chaos suppresses quantum coherence. The mean single particle coherence during the evolution is studied, and a better quantum-classical correspondence is obtained. Finally, the dynamics of single-particle coherence in the whole phase space is investigated, which reveals the chaotic and regular structures of the phase space more clearly.
Under the condition of classical limit,quantized Dicke model shows the dynamical behavior of quantum chaos.The numerical calculation shows that there are some particular points in the classical phase-space at which the quantum chaos is present.The impact of initial conditions of these particular positions on entanglement of the model was analyzed respectively under RWA(rotating-wave approximation) or non-RWA.The evolutionary characteristics of the overall dynamics were studied in the phase-space for all the phase points considered to be under the initial condition.The conclusion obtained is that classical chaos will accelerate the generation of entanglement.
Dicke model displays quantum chaotic dynamic properties in the non-rotating wave approximation. On the basis of properties of the classical phase space of Dicke model, we employ the one-to-many notion, namely, evolution from one point on the classical phase space to two initial coherent states. Then we obtain a good quantum phase space, which corresponds to the classical one, by using the method of averaging the statistical entangled values of two initial states in the evolution. The numerical computation shows that classical chaos can promote the origination of bipartite entanglement, and simultaneously, the average entanglement can be regarded as the signature of quantum chaos. A good classica-quantum correspondence can be obtained by using the average entanglement.
A quantum dicke model exhibits chaotic dynamic characters with the classical limit.By studying the quantum entanglement and quantum spin squeezing,such results are obtained :linear entropy that measuring the power of quantum entanglement,according to different initial states which corresponding to the different regions in phase space,have different behaviors: the power of quantum entanglement strengthen in the chaotic regions obviously and it is weak in the regular regions by contraries;the spin squeezing express difference between regular and chaotic regions in phase space,and the little probabilities of existing spin squeezing are in the regular regions absolutely.In the same conditions,there are exactly similar varieties of the linear entropies and the squeezing parameters.