混沌辅助的冷原子量子输运

发布时间：2018-05-02 15:14

本文选题：经典混沌 + 冷原子　；参考：《湖南师范大学》2016年博士论文

【摘要】：混沌行为是无所不在的,并在多个现代科学技术中发挥十分重要的作用。混沌科学还与其他学科相互渗透发展,并在物理学、数学、化学、生物学等领域得到了广泛的应用。此外,随着激光技术的发展,利用激光实现对单个原子的相干操控也吸引了越来越多的注意力,并在理论和实验研究中取的巨大的进展。在经典混沌系统中研究混沌与各量子行为的关系取得了一定的理论进展和实验突破,使其逐渐发展成一个热门话题。然而,混沌系统的经典-量子对应仍是一个极具挑战的难题。本学位论文基于混沌理论和量子力学相关理论,对囚禁在调幅并倾斜的光学晶格中的单个原子进行了比较系统的研究,并得到了一些有意义的结论,也为该系统的实验实现提供了可行性方案。全文共分为五章,第一章为绪论,在第二、三、四章中介绍了作者本人的研究工作,主要内容为：第一章为绪论部分,简单介绍了激光对原子的冷却和囚禁,光晶格系统,在紧束缚模型中原子的动力学现象以及混沌辅助的量子输运的研究进展。第二章,我们研究了囚禁在一维调幅并倾斜的光学晶格中的单个原子的经典特性和量子动力学。在经典混沌区域中我们分别定义了混沌有助于局域化和混沌有助于去局域化。我们还从解析上和数值上给出了跨越规则区域和混沌区域的近共振区域,并说明了近共振区域的宽度由系统的参数决定。根据混沌参数空间图,可知混沌区域的大小随着倾斜势的增大而减小。在Poincare截面中,势阱的中心区域由一些小幅的稳定岛组成,而这些稳定岛被混沌海分离。从经典的角度来说,局域在稳定岛中的粒子只会在该稳定岛中运动,而在稳定岛之间的跨越是不被允许的。经过量子处理,我们证实了当参数取在共振区域时,粒子会向晶格两端扩散,发生去局域化。因此,混沌有助于去局域化只发生在混沌与共振叠加的区域,而混沌有助于局域化发生在其他的混沌区域。调节倾斜势的大小以及调节参数点到近共振区域的距离大小可以控制局域化的程度。以上结果澄清了一个长期存在的矛盾“混沌是有助于局域化还是有助于去局域化”。在实验上,我们的结果也可以用于混沌辅助的囚禁在颤动的倾斜的光晶格或固态晶格中的粒子的量子输运。第三章,我们研究了混沌对囚禁在调幅和倾斜的光学晶格中的单个原子的量子输运的影响。在最近邻紧束缚近似下,通过求解含时薛定谔方程,我们得到了该系统的新的精确解,并导出了粒子的几率和平均位移的表达式。在本章中,我们分别定义了对应于混沌海的初始条件以及加入了位相的初始态。将多个初始条件和量子共振的参数应用到系统中,我们得到粒子不对称的平均几率分布,几率的不对称性导致了非零的双平均位移,表明发生了平均意义下的定向输运,这就是所谓的混沌辅助的定向输运。对于初始条件中任意给定的位相,粒子的输运速度与驱动强度正相关,粒子的输运方向则由倾斜势的符号决定。对于任意-组给定的参数,粒子初始态中的位相不仅可以改变粒子的输运速度,还可以改变粒子的输运方向。借助于相关的实验装置,从一个确定的原子源中将原子一个一个射入给定的光学晶格系统中,可以测得双平均位移的数值大小,由此可以证明我们得到的解析结果；根据所得的数值大小也可以确定粒子的位相。这些结果也可以直接延伸到与系统方程类似的不同的物理模型中,比如固态晶格系统、周期光波导和量子点阵。利用该系统模型及所得到的结果,我们可以制备一个“加速器”来帮助得到不同速度的粒子,还能设计一个量子开关来控制携带量子信息的单个粒子的输运方向。第四章,我们利用一个精确量子态的线性熵研究了囚禁在一维调幅和倾斜的光晶格中的单原子的内部电子态和外部运动态的量子纠缠动力学。首先,考虑一个非纠缠的初始态,该态的经典对应为经典相空间中的规则岛,我们证实了在量子共振的参数下会导致纠缠的产生,且与规则区域的参数相比,混沌区域的参数能够加大纠缠的增长速度；此外,初始几率分布的对称性决定了系统最终的纠缠度。其次,我们还考虑了经典对应为混沌海的纠缠初始态,再次发现系统最终的纠缠只与初始几率分布有关。这些结果在量子信息处理等领域可能具有重要的理论参考价值。第五章,我们对本学位论文的工作进行了总结,并对调幅并倾斜的光晶格系统中混沌对于量子输运的影响这一研究方向的发展前景作了简单展望。
[Abstract]:Chaos is omnipresent and plays a very important role in many modern science and technology. Chaos science is also widely used in the fields of physics, mathematics, chemistry, biology and other fields. In addition, with the development of laser technology, the coherent manipulation of a single atom is realized by laser technology. It also attracts more and more attention and has made great progress in theoretical and experimental research. The study of the relationship between chaos and each quantum behavior in the classical chaotic system has made some theoretical progress and experimental breakthrough, making it a hot topic. However, the classical quantum correspondence of chaotic systems is still a great one. This thesis is based on the theory of chaos and the theory of quantum mechanics. This thesis makes a comparative systematic study of the single atoms trapped in an optical lattice with amplitude modulation and tilt, and obtains some meaningful conclusions and provides a feasible scheme for the implementation of the system. The full text is divided into five chapters. The first chapter is the thread. In the second, third and four chapters, the author's own research work is introduced. The main contents are as follows: the first chapter is the introduction, which briefly introduces the laser cooling and imprisoning of atoms, the optical lattice system, the dynamics of atoms in the tight binding model and the progress in the chaos assisted quantum transport. In the second chapter, we have studied the imprisoning. In the classical chaotic region, we define the classical properties and the quantum dynamics of a single atom in an amplitude modulated and inclined optical lattice. In the classical chaotic region, we define that chaos helps localization and chaos help to delocalization. The width of the near resonance region is determined by the parameters of the system. According to the space map of the chaotic parameters, the size of the chaotic region decreases with the increase of the tilt potential. In the Poincare cross section, the central region of the potential well consists of some small stable islands, and these stable islands are separated by the chaotic sea. From the classical point of view, the local area is in the stable island. The particle will only move in the stable island, and the crossing between the stable island is not allowed. Through quantum processing, we confirm that when the parameter is taken in the resonance region, the particle will spread to the two ends of the lattice and occur delocalization. Therefore, chaos helps to delocalization only in the region of the superposition of chaos and resonance, and chaos helps. Localization occurs in other chaotic regions. Adjusting the size of the tilt potential and adjusting the distance between the parameter points to the near resonance region can control the degree of localization. The above results clarify that a long-standing contradiction "is chaos conducive to localization or delocalization". In experiment, our results can also be used. In the third chapter, we study the effect of chaos on the quantum transport of a single atom trapped in an amplitude and inclined optical lattice. In the nearest neighbour tight binding approximation, we obtain the system by solving the time-dependent Schrodinger equation. In this chapter, we define the initial conditions corresponding to the chaotic sea and the initial state of the phase. In this chapter, we apply the parameters of the initial conditions and the quantum resonance to the system, and we get the average probability distribution of the particle asymmetry and the probability of the particle. The asymmetry leads to the non zero double average displacement, which indicates that the directional transport under the mean sense is occurring, this is the so-called chaotic assisted directional transport. For any given phase in the initial condition, the transport velocity of the particle is positively correlated with the driving strength, and the transport direction of the particle is determined by the symbol of the tilt potential. With the given parameters, the phase in the initial state of the particle can not only change the transport velocity of the particle, but also change the transport direction of the particle. With the aid of the related experimental device, the numerical size of the double average displacement can be measured in a given optical lattice system from a determined atomic source. These results can also be extended directly to different physical models similar to the system equations, such as solid state lattice systems, periodic optical waveguides and quantum dots. "Accelerator" helps to obtain particles at different speeds and can also design a quantum switch to control the transport direction of single particles carrying quantum information. In the fourth chapter, we use the linear entropy of an exact quantum state to study the internal and external states of the single atom trapped in one dimensional amplitude modulated and tilted optical lattices. First, we consider a non entangled initial state. The classical correspondence of the state is the rule island in the classical phase space. We prove that the entanglement is caused by the parameters of the quantum resonance, and the parameters of the chaotic region can increase the growth rate of the entanglement in comparison with the parameters of the regular region. Moreover, the initial probability is also increased. The symmetry of the distribution determines the final entanglement of the system. Secondly, we also consider the initial state of the entanglement of the classical chaotic sea. It is found that the final entanglement of the system is only related to the initial probability distribution. These results may have important theoretical reference value in the field of quantum information processing. The fifth chapter, we discuss the theory of this degree. The work of this paper is summarized, and the prospect of the research direction of the influence of chaos on quantum transport in the amplitude modulated optical lattice system is prospected.

【学位授予单位】：湖南师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O415.5;O413.1

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