摘要
量子理论自二十世纪诞生以来,就开始深刻的影响和改变着人类社会,为了解和改造微观世界提供了理论基础,并推动了激光、半导体、核能等高科技的发展。量子理论在快速发展的同时,不断与其他学科交叉融合,量子控制就是量子理论与控制科学相结合产生的一门新兴学科,量子控制的迅速发展必将带来科学界的又一次革命。以研究量子系统主动控制为主要内容的量子控制理论诞生了。量子控制作为一个全新的学科领域正在蓬勃崛起。它的发展可能彻底改变计算机,工业,医学与生命学科。量子控制系统应用与化学反应的研究也有很多成果。其中激光作为重要的实验工具,极大的促进了量子相干控制理论的发展。
本论文的主要工作是研究和讨论量子控制中的多能级哈密顿系统在激光脉冲驱动下的有效维约化。我们考虑了近能级简并的影响,对不同强度激光脉冲控制场下的多能级系统的布居转移,讨论了量子控制中的一些基本观念和方法,介绍旋转波近似和微扰近似的适用范围,以及二能级系统中的拉比振荡。我们对薛定谔表象下的二能级模型进行了详细的分析,并详细讨论多能级系统模型的一般理论,研究在外界脉冲驱动控制下的多能级系统的量子动力学情况,全面地讨论了脉冲驱动的多能级系统的模型,以及不同强度激光场控制下的多能级的布居转移情况。
我们主要研究了在外界脉冲驱动控制下的存在近简并能级的多能级系统的量子动力学,讨论了不同激光场控制下的基态到近简并多能级激发态的布居转移,指出在不同强度激光控制下的近简并多能级与二能级系统间的布居转移的相似性,从理论上证明了在外界控制场满足一定条件时,所考虑的多能级的布居转移结果和二能级的相似,以上结果可以推广到有多组近简并能级的多能级系统,用来简化设计一般意义上的有限维量子系统的控制策略。
Quantum theory has changed the landscape of human society since it was found in the 20th century. It established the foundation for understanding and explaining phenomena in atomic and sub-atomic scale, and promoted the development of laser, semi-conductor, nuclear power and so on. During its development, Quantum theory is fusing with other branches of science. Quantum control is a new area of science born from the combination of quantum theory and control theory. It may bring in revolution to computer science, medical and life science. The application of quantum control in chemical reaction has already produced exciting achievements and the invention of laser, and further accelerated the development of the theory of quantum coherent control.
This thesis discusses how the dimension of a multi-level quantum system is reduced to a simple system when it is controlled by a short laser pulse. We consider the effect of near degenerate eigenstates, and the strength of the laser. The objective is to control the collective population on all excited states. We treat the system with Rotating Wave Approximation (RWA) and perturbative theory. Precise and approximate model of pulse-driven two-level systems are studied and compared with the original multi-level systems. The population transfer of multi-level quantum system controlled by short pulsed is analyzed in different situation.
In the thesis, we focus on the multi-level quantum system with near degenerate eigenstates, and discuss the population transfer from the ground state to the near-degenerate excited states. It is noted that in the case of both weak and strong field, the multi-level system can both be reduced to a two-level system. The results could be generalized to a multi-level system with several sets of near-degenerated eigenstates. The conclusion could be utilized to identify the effective dimension of a quantum multi-level system controlled by laser.
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