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.
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.
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.
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.
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.
The quantum information is a new interdisciplinary science in the 21st century, and it has become a research field which attracts strongly much attention in the world. Recently, the study of the quantum computer is in the ascendant. In the process of finding a scheme for quantum computation, quantum chaos aroused much attention. It has been shown that it is possible to induce quantum chaos when running quantum computer and consequently it may destroy the operational condition of the quantum computer. The relationship between quantum entanglement and quantum chaos has already been investigated, and the spin squeezing is regarded as another classical quantum property indeed, then is there a natural relationship between quantum chaos and spin squeezing? In this paper a very typical QKT model in the quantum chaos has been discussed,and the properties of spin squeezing in the quantum chaotic system has been studied. The relation between spin squeezing parameters and chaotic parameter in the two different definitions is worked out by numerical calculation. The stronger that the regular regions are than chaotic ones, which are chosen firstly, in the classical phase space, the stronger the spin system which the initial states locate at the centre of elliptical regions as a result. If the initial states are chosen another condition, the contrary result is obtained naturally. It indicates the spin squeezing is very sensitive to the classical chaos and the classical chaos suppresses the spin squeezing. It is interesting that the definition by Wineland is more sensitive than the one by Kitagawa and Ueda, consequently a conclusion, which the quantum chaos can be described by spin squeezing, is acquired.
In this paper, by using QKT model, we give the changing relation between chaotic coefficient k and spin squeezing coefficient of two different definitions by numerical simulation calculation. The results show that the regular regions are stronger than chaotic ones in the classical phase space, the spin squeezed behavior is very strong, and the chaotic regions are stronger than regular ones in the classical phase space, the spin squeezed behavior is very weak, which indicate the spin squeezing is very sensitive to the corresponding classical chaos. Through the comparison we also know that the spin squeezing coefficient defined by Wineland is more sensitive to the classical chaos than the one by Kitagawa and Ueda, so the quantum chaos can be described by spin squeezing.
We study spin squeezing, an intrinsically quantum property, in the quantum kicked top model exhibiting chaotic behaviours in the classical limit. We show that spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a sphere with a unit radius, namely, spin squeezing vanishes after a very short time for an initial spin coherent state centred in a chaotic region of the phase space, whereas spin squeezing occurs over a long period of time for the coherent state centred in an elliptic fixed point. We also study the distribution of the mean spin directions when quantum dynamics take places and give a comparison between the dynamics of spin squeezing and quantum entanglement.