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Acta Physica Sinica

Quantum chaos and the dynamic properties of single-particle coherence in Dicke model

Song Li-Jun, Dong Yan, Gai Yong-Jie, Wang Yu-Bo, (1)长春大学理学院，长春 130022; (2)长春理工大学理学院，长春 130022

Published Jan 1, 2010• 7 citations
Publisher

Abstract

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.

DOI
10.7498/aps.59.3695

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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.
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.
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.
The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time t, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.
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.
We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.
Fisher information is an important concept in estimation theory, which has recently been found closely related with the criteria of the entanglement in quantum information. Under the condition of non-rotating wave approximation, the classical phase space of the Dicke model displays chaotic dynamic properties. This paper studies the quantum Fisher information and the dynamic properties of spin squeezing in the interaction system of light and matter described in the Dicke model. Results reveal that, in the short-time instant state, wherever the initial state is, in a regular region or a chaotic region, the system displays entanglement; but in the long-time stable state, when the initial state is in the regular region, the system entanglement disappears, however, when the initial state is in the chaotic region, the system is always entangled. Compared with the spin-squeezing dynamic properties of the system, Fisher information is found to be able to effectively characterize quantum chaos. On further examination on the dynamic evolvement properties of the density matrix and purity of the system when in the regular and chaotic regions, we find that chaos gives rise to decoherence of the system, showing that quantum information become more sensitive to chaos.