量子路径在封闭系统中的优化控制及开放系统中的编码方法研究

发布时间：2018-04-25 23:11

本文选题：HE-OD + 路径跃迁　；参考：《中国科学技术大学》2017年硕士论文

【摘要】：量子路径描述了量子系统动力学的细节,是表征量子控制机理的一个重要手段,具有重要的物理意义。对于封闭多能级系统的研究,我们从不同量子路径的相干相长效应出发,研究如何提高初始态到目标态的布居转移效率。封闭系统和开放系统的量子路径的信息可在哈密顿量编码-观测量解码方法的框架下进行研究。在封闭系统中,由于不存在环境作用,其哈密顿量编码方案比较简单,其量子路径的解码结果可以和Dyson展开项保持一致。封闭系统可在Hilbert空间进行描述,而开放系统则要转换到Liouville空间。此时环境作用将同时出现在演化方程中哈密顿量的对角元和非对角元上,常规的用于封闭系统的编码方案会导致量子路径的解码结果与积分的Dyson项结果不一致。因此,本论文通过分析与对比两种方法路求解径跃迁幅度的的区别与联系,提出了一套新的哈密顿量编码方案,能够巧妙避免哈密度量编码-观测量解码方法产生的自身到自身的"非物理"跃迁,同时使得量子路径的解码结果与Dyson项保持精确对应。具体工作如下:1.Lee的八分块方案能够优化四能级Rb原子的双光子吸收强度。分块的边界点由一个多项式方程的根给出。我们把此方法推广到五能级,同时也又提出了一种新的全局最优的分块方法,并给出了数学上严格的推导和证明。最后把每个数值模拟的结果都与转换极限(TL)脉冲进行了对比,数据结果表明多能级系统的分块方案都可以有效的增强双光子(TPA)路径振幅。此部分内容为第二章。2.对HE-0D方法在开放量子系统中的使用做了进一步较为详细的讨论,而后又从基本的量子力学出发计算路径幅度。当发现二者有差别的时候,文中又提出了一些分析和解释。当对原矩阵的部分对角线上的元素也进行编码后,二者之间的差别也在逐步缩小。出现了一些发生在自身能态中的跃迁能级,可是他们从物理意义上并没有相应的解释。此部分内容在第三章。3.在本文中出现了一些没有实际物理意义的跃迁,所以接下来将会相应的提出一些解决方法,由于其数学形式比较复杂,所以首先对二能级开放量子系统进行研究,其中分别分析了极端情况下当电场为零的和普遍情况下电场不为零的情况,而且通过相应的数学转变,就可以成功的把对角线元素消除掉,这样就可以避免了第三章中出现的一些奇怪的跃迁路径。进一步将这种思想拓展到三能级开放量子系统中,也分别做了相应的分析和证明,结果同样也可以得到与二能级开放量子系统相同的情况。数值结果表明HE-OD解码得到的路径幅度与Dyson积分结果一致。此部分内容在第四章。
[Abstract]:Quantum path describes the details of quantum system dynamics and is an important means to characterize quantum control mechanism. It has important physical significance. For the study of closed multi-level systems, we study how to improve the population transfer efficiency from the initial state to the target state based on the coherent phase length effect of different quantum paths. The quantum path information of closed system and open system can be studied under the framework of Hamiltonian encoding and observation decoding method. In the closed system, the Hamiltonian coding scheme is simple, and the decoding result of the quantum path can be consistent with the Dyson expansion term. Closed systems can be described in Hilbert spaces, while open systems are converted to Liouville spaces. In this case, the environmental action will occur on both diagonal and non-diagonal elements of Hamiltonian in the evolution equation. The conventional coding scheme for closed systems will cause the decoding result of quantum path to be inconsistent with the Dyson term of integral. Therefore, by analyzing and comparing the differences and relations between the two methods, we propose a new Hamiltonian coding scheme. It can avoid the "non-physical" transition from itself to itself generated by the Hami metric coding and measurement decoding method, while keeping the decoding result of quantum path exactly corresponding to the Dyson term. The main work is as follows: 1. Lee's eight-block scheme can optimize the two-photon absorption intensity of a four-level RB atom. The boundary point of a block is given by the root of a polynomial equation. We extend this method to five levels, and at the same time, we propose a new global optimal partitioning method, and give a strict derivation and proof in mathematics. Finally, the results of each numerical simulation are compared with the conversion limit (TL) pulse. The results show that the block scheme of the multi-level system can effectively enhance the amplitude of the two-photon TPA path. This part is the second chapter. 2. The application of HE-0D method in open quantum systems is discussed in detail, and then the path amplitude is calculated from the basic quantum mechanics. When it is found that there is a difference between the two, some analyses and explanations are presented. When the elements on the diagonal line of the original matrix are also coded, the difference between them is gradually reduced. There are some transition energy levels which occur in their own energy states, but they have no corresponding explanation in the physical sense. This part is in Chapter 3. 3. In this paper, there are some transitions which have no actual physical meaning, so we will put forward some corresponding solutions. Because its mathematical form is more complicated, so we first study the two-level open quantum system. The case of zero electric field in extreme case and non-zero electric field in general case is analyzed respectively, and the diagonal element can be eliminated successfully by corresponding mathematical transformation. This avoids some of the strange transition paths that appear in Chapter 3. This idea is further extended to the three-level open quantum system, and the corresponding analysis and proof are made, and the same result can be obtained as the two-level open quantum system. Numerical results show that the path amplitude obtained by HE-OD decoding is consistent with that of Dyson integral. This part is in the fourth chapter.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O413;O231

【参考文献】