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1、吉首大学硕士学位论文囚禁离子质心运动的激光控制姓名：江敏申请学位级别：硕士专业：凝聚态物理指导教师：邬云文20100501摘 要 第 i 页 摘 要 摘 要 自上世纪五十年代离子阱出现以来，离子阱已广泛应用于科学和技术研究的各个领域。尤其近二十年来，随着激光冷却技术以及其它相关的技术的出现和发展，离子阱作为一种有效的工具，在量子逻辑门，量子态制备，量子计算和量子信息等领域有重大的应用。人们通过控制囚禁离子与光场的相互作用，可以精确地操控囚禁离子的内态和外态，这为实现量子计算、量子通信等提供了可靠的理论和实验依据。 目前，对于囚禁离子的研究主要有以下几个方面：无外加激光作用下，单离子体系、两离子
2、体系以及多离子体系的经典与量子动力学特征研究；各种外加激光场与囚禁单离子体系相互作用的经典和量子特性研究，如各种量子态的制备等。但是对于外加激光作用下囚禁多离子的运动特性、多离子质心的运动特性研究较少。而质心运动的研究，对实现量子逻辑门、囚禁离子的边带冷却与加热、囚禁离子的双模非经典态的制备等有一定的参考意义。由于两离子系统，是多离子系统研究的基础，相对来说比较简单，易于计算处理。因此我选用 Paul 阱中两离子系统作为研究对象，主要研究系统在不同参数和初始条件下，囚禁离子质心与激光相互作用的动力学特征，以及囚禁离子质心量子运动问题。具体内容如下： 第一章中，主要介绍了 Paul 阱的基本原理
3、以及囚禁离子激光控制的研究历史和现状。 第二章中，主要研究了一个外加周期驱动激光场的两离子系统的质心动力学特征。在赝势近似条件下，运用经典处理方法，通过受控离子质心的经典运动方程，得到了囚禁离子质心运动轨道的精确解析解。为研究囚禁离子的受控条件，我们运用数值计算和计算机模拟的方法，对离子处在不同的初始条件、阱频强弱以及相互作用时间等因素下，离子质心运动所受到的影响做了分析研究。结果表明，囚禁离子的初始状态、囚禁阱频率对限制囚禁离子质心运动的范围，振荡幅度有影响，囚禁离子与激光的相互作用时间，可以影响离子质心运动的模式；通过作出的囚禁离子质心运动的相空间轨道图，提出了囚禁离子质心做规则运动以及混
4、沌运动的所需外部条件。 第三章中，从量子力学的角度，我们研究一个考虑库仑关联并受一个外加周期驱动激光场所驱动的两离子系统，研究其囚禁离子质心运动态的跃迁控制问题。运用我们所熟知的微扰法，计算出了此两离子系统的质心运动态（声子态）跃迁几率的解析表达式，并模拟出了声子态跃迁几率随激光束频偏和相互作用时间变化的分布图形。结果表明，在弱场的作用下，随着外加周期驱动激光场的频率和相互作用时间的调节，系统质心振动声子态随时间周期性的坍塌与复原，频偏过摘 要 第 ii 页 大时，激光束不能有效控制质心量子态的跃迁。 第四章是对本论文研究工作的总结，并对 Paul 阱中囚禁离子的动力学研究做了一个展望。 主题
5、词：囚禁离子，Paul 阱，激光脉冲，微扰法，规则与混沌运动，跃迁几率 ABSTRACT 第 iii 页 ABSTRACT ABSTRACT Ion traps have been used in scientific and technological research in various fields widely since the invention of ion trap the fifties last century. In the past two decades, With development of the laser-cooling technology and th
6、e appear of other new technologies related to ion trap, as an effective tool , Ion traps get a significant application in the quantum gates, quantum state, quantum computing and quantum information. By using the interaction of trapped ions and laser pulse, we can manipulate not only the internal sta
7、tes, but sale the external states with very high precision, which makes trapped-ion system ideally suited for quantum computing, quantum communicat- ion and so on under well-controlled conditions. There are many researches on trapped ions recently. Mainly as follows: the characteristics of classical
8、 and quantum dynamics of the single-ion system 、two-ion system and multi-ion system without interaction of external laser; the characteristics of classical and quantum of the interaction that between trapped single-ion system and external laser, such as a variety of quantum states researches. But th
9、ere are less researches on characteristics of motion of multi-ion system and mass center of multi-ion system. Whereas, the motion of center of mass researches have a certain reference value on the realization of quantum logic gate, trapped ions sideband cooling and heating, as well as preparation of
10、 dual-mode non-classical states. As the two-ion system is the basis of multi-ion system, it is more simple relatively and easy to be computed. So I chose the two-ion Paul trap system for our researches, and mainly we have studied the motional dynamics characteristics of interaction between mass cent
11、er of trapped ion and external laser with different parameters and initial conditions, and aslo we have studied the quantum motion aspects of mass center too. Details are as follows: In the first chapter, the basic principle of the Paul trap is briefly introduced, and the history and progress on the
12、 researches of interaction between trapped ions and laser fields is presented. In the second chapter, we have studied a two-ion system, which the trapped ions couple to a external periodical laser field. Under the pseudo-potential approximation condition, by using the classical approach, we solved c
13、lassical motion equation, and we have figured out its precise analytical expression of center-of-mass motion of trapped-ion. In order to find out the well-controlled conditions, we have analyzed the influence aroused by different initial conditions, the trap frequencies as well as interaction time b
14、y taking numerical calculation and computer simulation methods. The results show that the initial state of a trapped ion、trap frequency limit the motional ABSTRACT 第 iv 页 range or oscillation amplitude of mass center, and the interaction time can affect the motional model. Meanwhile, we have plotted
15、 the orbits on phase space, and proposed required external conditions that to do regular and chaotic motion of the trapped ions. In the third chapter, from the perspective of quantum mechanics, considering two trapped-ion system with the ions stored in a linear Paul trap, and taking the coulomb inte
16、raction and external periodical laser field that the system subjected to into account, we have studied the issue about controlling of trapped-ion center-of-mass (phonon state) transition. Using our well-known perturbation method, we figured out its analytical expression of states of center-of-mass (phonon state) transition probability. And we also simulate the phonon state transition probability distribution graph relates to frequency offset and int
