【作者】 黄俊；

【导师】 侯喜文；

【作者基本信息】 华中师范大学 ， 原子与分子物理， 2013， 硕士

【摘要】 随着量子信息技术的发展,量子纠缠理论的研究也越来越得到了人们的重视。我们首先介绍量子纠缠理论的基础知识,着重说明量子纠缠态的定义、可分性判据、纠缠程度的度量方法和几种常见的纠缠度,还简略的介绍了量子纠缠理论在量子信息领域的应用。我们以约化密度矩阵和矩阵的部分转置为基础方法,详细地研究了Tavis-Cummings模型中的三组分量子纠缠动力学,其中采用负性纠缠与所谓的3-π纠缠为纠缠度量。我们着重分析该模型初态所处的状况以及原子与腔场之间相互作用的耦合系数、原子与环境相互作用的衰减率等参量对其纠缠演化特性的影响,还详细的分析与比较了该模型中负性纠缠度与所谓的3-π纠缠度的关联状况。进而得到以下结论：在T-C模型中,其纠缠度随时间的演化特性主要取决于其哈密顿量中的衰减率和耦合系数以及其初态的概率幅。与环境相互作用的衰减率始终影响着其纠缠度波动式下降的快慢。耦合系数则主要影响其纠缠随时间演化的振荡频率。该T-C模型的初始态中各组分的概率分布主要影响其纠缠随时间演化的振荡振幅。通过改变其初始态中各组分的概率幅,可以控制其纠缠度振荡的幅度,在|eg0>和|ge0>态的概率为a2=b2=1/4的情况时,其纠缠度随时间演化的曲线将会变成一条直线,其振荡行为消失且单个分量的负性纠缠度Nc将保持最大值。对T-C模型中负性纠缠度与3-π纠缠度的关联性研究表明,在合适的条件下这两种纠缠度是完全正相关的。这些研究有利于多组分量子纠缠理论和量子信息的发展。更多还原

【Abstract】 With the development of quantum information technology, more and more attention has been paid on the study of quantum entanglement. In this paper, we will summarize the basics theory of quantum entanglement. First we introduce the definition of quantum entangled states, the separability criterion, the quantum entanglement measure, and cite a number of entanglement measures. The applications of entanglement in the field of quantum information are introduced as well.We use the reduced density matrix and the partial transpose matrix to analysis the tripartite entanglement of negative and three-π entanglement measure in the Tavis-Cummings model. We consider the influence of the initial state, the coupling coefficient, the decay rate on the evolution properties of entanglement. Also, we analyze the influence on the dynamical correlation between negativity and the three-π measure. We have some conclusions.In the Tavis-Cummings model, the evolution properties of the entanglement is mainly determined by the decay rate and the coupling parameter. The decay rate determines the declining trend of the entanglement curve, and the coupling determines its frequency of the evolution of entanglement.In the Tavis-Cummings model, the probability amplitude of the initial states influence on the amplitude of the entanglement curve. It is still shown that when the coefficients of the initial state|egO>|geO> are a2=b2=1/4, the oscillation of the entanglement will be disappear, and the Nc will maintain the maximum.For the dynamical correlation of negativity and the three-π entanglement measure, it is shown that under suitable conditions, those two entanglements are positively correlated.Those are useful for multipartite entanglement and quantum information.更多还原