玻色—爱因斯坦凝聚系统的混沌控制与同步研究

发布时间：2018-06-17 12:53

本文选题：玻色—爱因斯坦凝聚 + 光学晶格　；参考：《长春理工大学》2017年博士论文

【摘要】：玻色—爱因斯坦凝聚(Bose-Einstein condensation,简称BEC)是一类涉及物理学诸多领域的普遍物理现象。1924年在玻色的启发下,爱因斯坦预言了当温度足够低时服从玻色统计的理想中性原子气体将发生凝聚现象。由于实现BEC的条件非常苛刻,直至1995年,人们才通过激光冷却、静磁阱与蒸发冷却等技术实现了近理想气体碱金属原子的BEC。BEC是由上万乃至上百万原子构成的宏观量子系统,它的原子完全失去了孤立粒子的特征。BEC将量子现象带到宏观尺度,其物质波可由单一的宏观波函数来描述。随着BEC在实验中的实现,该领域的相关研究逐渐成为了科学领域的热门研究课题。利用激光的相干叠加形成的光学晶格也为人们便利而又精确操纵BEC提供了一个非常有效的工具。它在BEC的研究中应用广泛,光学晶格与BEC的结合为我们开拓了许多新的研究方向。BEC是一个研究量子力学基本问题的宏观系统,它在原子钟、原子激光、量子计算、量子信息处理等很多领域有着重要的应用。作为一个典型的非线性系统,混沌在BEC中的存在已经得到证实。鉴于这种凝聚物质广泛的应用前景,基于混沌对BEC稳定性的影响,为了更好的利用和操控BEC,对BEC系统的混沌产生、控制及同步的研究是非常有价值的工作。该研究对凝聚体的合理利用以及新材料的研制都具有极其重要的意义。本文基于Gross-Pitaevskii(G-P)理论形式的弱相互作用玻色理论,以原子的Hartree-Fock平均场理论框架下的G-P方程为主要模型,主要对装载在运动光学晶格中具有阻尼效应的BEC系统的混沌特性、混沌控制和混沌同步问题进行研究。另外,对一维斜光学晶格BEC系统的混沌行为、混沌控制及混沌同步进行了有益的探讨。主要包括以下几方面内容:1.首先系统地介绍了非线性系统中混沌理论、混沌控制、混沌同步研究的发展历史。对本论文的研究BEC系统及其性质、BEC中的混沌研究进展进行介绍。2.主要研究了运动光学晶格中原子间呈相互吸引作用的BEC原子的稳定性和空间混沌行为。通过理论和数值分析,得出系统的混沌区域的参数范围。数值计算结果给出了一定参数条件下系统随不同参数变化时的最大李雅普诺夫指数(Lyapunov exponent)图、分岔图、混沌吸引子、时间序列及功率谱,进一步阐明了运动光学晶格BEC的混沌特征。3.提出了实现BEC系统混沌控制的四种方法,即常数偏移法、周期驱动力法、小波函数控制法和线性反馈法。通过数值模拟分别计算利用上述四种方法时的最大Lyapunov指数随控制参数变化图和分岔图。由Lyapunov稳定性理论可知,只有最大李雅普诺夫指数为负值时,系统才会处于稳定态。并给出控制参数取不同值时的周期轨道所对应的相空间吸引子图和时间序列图,从而用数值计算结果验证了所提方法的有效性。4.研究了两个BEC系统的混沌同步或反同步。利用Lyapunov稳定性理论、线性稳定性理论及Routh-Hurwitz判据,理论分析了正弦耦合、线性耦合、双曲正弦耦合和激活控制法实现BEC系统的混沌同步或反同步演化过程,并得到能实现混沌同步的各种耦合参数的条件,通过数值计算证明上述方法的可行性和有效性。并分析了混沌同步时间和控制参数之间的关系,为实现运动光学晶格BEC系统的混沌同步和反同步提供几种有效的方法。5.对一维斜光学晶格中BEC系统的动力学方程进行数值求解,由吸引子图和时间序列图说明此系统具有的混沌特征。讨论倾斜因子、光学晶格振幅及初始条件对此光学系统的混沌运动的影响,并分析了采用常数偏移法实现混沌控制的效果,从而找到实现系统混沌控制的可行性方法。最后,对本文的研究工作进行归纳和总结,对玻色—爱因斯坦凝聚这一领域的研究发展前景进行展望,从而为下一步深入研究找到新的方向。
[Abstract]:Bose-Einstein condensation (Bose-Einstein condensation, BEC) is a kind of universal physical phenomenon involving many fields of physics. Under the illumination of Bose, Einstein predicted that the ideal neutral atom gas, which obeys the Bose statistics when the temperature is low, will produce the phenomenon of condensation. Because the conditions for realizing BEC are very harsh, Until 1995, it was only by laser cooling, static magnetic trap and evaporative cooling that the BEC.BEC of the alkali metal atoms of the near ideal gas was a macroscopic quantum system consisting of tens of thousands or millions of atoms. Its atoms completely lost the characteristic.BEC of the isolated particles and brought the quantum image to the macroscopic scale. With the realization of the macro wave function, with the implementation of BEC in the experiment, the related research in this field has gradually become a hot research topic in the field of science. The optical lattice formed by the coherent superposition of laser also provides a very effective tool for people to manipulate BEC conveniently and accurately. It is widely used in the study of BEC, optical lattice. The combination with BEC has opened up a lot of new research directions,.BEC is a macro system to study the basic problems of quantum mechanics. It has important applications in many fields, such as atomic clocks, atomic lasers, quantum computing, quantum information processing, and so on. As a typical nonlinear system, the existence of chaos in BEC has been confirmed. The wide application prospect of the condensed matter is based on the effect of chaos on the stability of BEC. In order to make better use of and manipulate the BEC, it is of great value to study the chaos generation, control and synchronization of the BEC system. This study is of great significance to the rational utilization of condensate and the development of new materials. This paper is based on Gross. The weak interaction Bose theory in the form of -Pitaevskii (G-P) is used as the main model of the G-P equation under the framework of the atomic Hartree-Fock mean field theory. The chaotic characteristics, chaos control and chaotic synchronization of the BEC system with damping effect loaded in the moving optical lattice are studied. In addition, the one-dimensional oblique optical lattice BE is also studied. The chaotic behavior, chaos control and chaos synchronization of C system are discussed. The main contents are as follows: 1. first, the development history of chaos theory, chaos control and chaos synchronization in nonlinear systems is introduced systematically. The research on the BEC system and its properties in this paper, and the progress of chaos in BEC are introduced.2. The stability and spatially chaotic behavior of BEC atoms with mutual attraction between atoms in a moving optical lattice are mainly studied. Through theoretical and numerical analysis, the parameters range of the chaotic region of the system is obtained. The numerical results give the maximum Lee Yap Andrianof exponent (Lyapuno) of the system with varying parameters under a certain parameter. V exponent) diagram, bifurcation diagram, chaotic attractor, time series and power spectrum, further elucidate the chaotic characteristics of BEC in the motion optical lattice.3., and put forward four methods to realize chaos control of BEC system, namely, constant offset, periodic driving force method, wavelet function control method and linear feedback method. The maximum Lyapunov exponent of the method is with the control parameter change graph and the bifurcation diagram. It is known from the Lyapunov stability theory that only when the maximum Lee Yap Andrianof exponent is negative, the system will be in the stable state. The phase space attractor and time series diagram corresponding to the periodic orbit of the control parameters are given, and the numerical value is given. The computational results verify the effectiveness of the proposed method.4. studies the chaotic synchronization or anti synchronization of two BEC systems. Using the Lyapunov stability theory, the linear stability theory and the Routh-Hurwitz criterion, the sinusoidal coupling, linear coupling, hyperbolic sinusoidal coupling and activation control are theoretically analyzed to realize the chaotic synchronization or anti synchronization evolution of the BEC system. The conditions of various coupling parameters that can be synchronized with chaos are obtained. The feasibility and effectiveness of the proposed method are proved by numerical calculation. The relationship between the synchronization time and the control parameters is analyzed. Several effective methods for realizing the chaotic synchronization and anti synchronization of the moving optical lattice BEC system,.5., are provided for one dimension oblique light. The dynamic equations of the BEC system in the lattice are numerically solved. The chaotic characteristics of the system are illustrated by the attractor diagram and the time series diagram. The influence of the tilt factor, the optical lattice amplitude and the initial conditions on the chaotic motion of the optical system is discussed, and the effect of the chaos control by the method of constant migration is analyzed, and the reality is found. In the end, the research work of this paper is summarized and summarized, and the prospect of the Bose Einstein condensation in this field is prospected, so as to find a new direction for further research.
【学位授予单位】：长春理工大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O415.5

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