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1、安徽大学 硕士学位论文 相干态在量子信息处理中的应用研究 姓名：汪贤才 申请学位级别：硕士 专业：材料物理与化学 指导教师：杨名;曹卓良 2010-04 摘 要 1 摘摘 要要 在量子光学中，运用 Jaynes-Cummings 模型光场与原子相互作用系统的非 经典特性研究一直受到关注。 本文应用全量子理论和数值计算方法来研究相干态 光场与原子相互作用的动力学特性； 运动原子与相干态光场相互作用光场压缩效 应、运动原子与相干态光场相互作用反聚束效应；型三能级原子与相干态光场 大失谐作用获得最大纠缠态和制备任意相干量子叠加态、 实现非最大纠缠态的纠 缠浓缩，得出了一系列有意义的结论。 第一章简要
2、介绍光场与原子相互作用的基本理论，相干态光场形式、光场与 原子作用的几种理论模型、推广的 Jaynes-Cummings 模型、纠缠度与非最大纠 缠态的纠缠浓缩和纯化。 第二章运用数值计算方法和全量子理论研究相干态光场与运动二能级原子 相互作用系统的光场压缩效应、 双模纠缠相干态光场与运动三能级原子相互作用 系统的反聚束效应。具体讨论了原子运动速度变化、基态模参数和相位角对光场 压缩特性的影响。结果表明： （1）原子运动速度的增大使曲线周期逐渐变小，光 场由部分压缩到刚好完全压缩转化到不压缩；随着相干态光场基态模参数的增 大，光场由完全压缩到部分压缩乃至完全不压缩；相位角的增大，光场随之由不
3、压缩逐渐变为部分压缩然后出现刚好完全压缩最后又到不压缩。 （2）研究双模纠 缠相干光场与运动三能级原子相互作用过程中的结果表明：平均光子数较小时， 双模纠缠相干光场的纠缠度和原子初态变化引起曲线振荡幅度变化，产生弱关 联；平均光子数取一定数值，原子运动速度增大导致时间演化曲线显著上移，振 荡周期变小，引起系统较强的反聚束效应；当平均光子数较大时，双模纠缠相干 光场的纠缠度和原子初态对演化曲线不产生任何影响；平均光子数变动不大，系 统就可由聚束效应跃变为反聚束效应，关联最强。 第三章在腔量子电动力学体系中,运用相干态光场与型三能级原子大失谐 作用： （1）在经典场辅助作用下，以此最大纠缠态作为量
4、子通道远程制备可随意 操控的相干态光场任意叠加态。经过计算，得出对于叠加系数为实数的相干态光 场的叠加态，通过适当旋转操作，远程制备成功的概率是 100。最后讨论了实 验上实现此方案的可行性和所具备的应用优势。 （2）通过纠缠交换，无须联合贝 相干态光场在量子信息处理中的应用研究 2 尔态测量，就可以实现原子与原子、原子与光场、光场与光场之间的非最大纠缠 态纠缠浓缩；如果使用 concurrence 作为纠缠度量，本方案的平均输出纠缠度是 初始两个非最大纠缠态纠缠度的乘积，而不是二者之和，在此过程中激发态原子 自发辐射的影响由于量子信息编码在两个简并基态和大失谐作用被绝热地消除。 第四章对全文
5、进行了总结并对相关问题进行了展望。 关键词：相干态 运动原子 光场压缩 反聚束效应 远程态制备 纠缠浓缩 Abstract 3 Abstract In the context of quantum optics, the study of quantum properties for the interaction between optical field and atoms has attracted much attention. It is one of the most important contents of quantum optics to study the dynamic
6、s and the non-classical properties of optical fields and atoms in the Jaynes-Cummings model with the interaction between the fields and atoms. In this thesis, the optical field squeezing effects of the optical fields in the system of the coherent states field interacting with a moving two-level atom
7、, and the photon antibunching effect in the system of two-mode entangled coherent states interacting with a moving V-type three-level atom are invetigated here; the maximally entangled state between the atom and the coherent optical field are prepared by the highly detuned interaction between three-
8、level -type atom and coherent optical field, an arbitrary superposition of a pair of coherent states can be remotely prepared with the aid of entangled coherent states freely, the entanglement concentration for non-maximally entangled states between atoms and atoms, atoms and optical fields, optical
9、 fields and optical fields have been realized via entanglement swapping without the joint Bell states measurement. A series of significant results are obtained. In chapter 1, the elementary theories upon the interaction between optical fields and atoms are introduced, the form of the coherent states
10、, several kinds of theoretical models, several kinds of quantum logic gates, the measure of entanglement and the entanglement concentration for non-maximally entangled states. In chapter 2, we study the optical field squeezing effects for moving atoms interacting with the coherent optical field and
11、the photon bunching and antibunching effect in the system of the two-mode entangled coherent states interacting with a moving V-type three-level atom by using the quantum theory and the numerical calculation method. The result are obtained as follows:(1) With the increasing of atomic speed, the curv
12、e period is gradually shortened, and the optical field squeezes change from the partial squeeze to complete squeeze, and finally to zero squeeze ; with compression factor increasing, the curve periods will not obviously change, 相干态光场在量子信息处理中的应用研究 4 but the curve oscillation amplitude obviously incre
13、ases actually, i.e. the squeeze stability becomes small; with the phase angle increasing, the squeeze effects of optical field vary from zero squeeze to partial squeeze, then to complete squeeze, and then to zero squeeze again；with the increasing of the ground state model parameter, the optical fiel
14、d is squeezed completely initially, and then partially squeezed, and finally it is not squeezed; (2) The initial state of the atom and the degree of entanglement of the two-mode entangled coherent states only have slight influences on the effect of photon bunching and antibunching, for those relativ
15、ely large mean photon numbers,the initial state of the atom and the degree of entanglement of the two-mode entangled coherent states have no influences on the effect of photon bunching and antibunching. For those relatively small mean photon numbers,the effect of photon bunching and antibunching in
16、the system intensively depend on mean photon numbers of the two-mode entangled coherent states and the speed of the atom. For a special mean photon number, the velocity of atom will afftect the effect of photon bunching and antibunching dramatically. In chapter 3, Using the highly detuned interaction between the three-level -type atom and the coherent optical field in cavity QED: (1)The maximally entangled state between the atom and the coherent optical field can be prepared. With the
