本文選題：HE-OD + 路徑躍遷　； 參考：《中國(guó)科學(xué)技術(shù)大學(xué)》2017年碩士論文

【摘要】：量子路徑描述了量子系統(tǒng)動(dòng)力學(xué)的細(xì)節(jié),是表征量子控制機(jī)理的一個(gè)重要手段,具有重要的物理意義。對(duì)于封閉多能級(jí)系統(tǒng)的研究,我們從不同量子路徑的相干相長(zhǎng)效應(yīng)出發(fā),研究如何提高初始態(tài)到目標(biāo)態(tài)的布居轉(zhuǎn)移效率。封閉系統(tǒng)和開(kāi)放系統(tǒng)的量子路徑的信息可在哈密頓量編碼-觀測(cè)量解碼方法的框架下進(jìn)行研究。在封閉系統(tǒng)中,由于不存在環(huán)境作用,其哈密頓量編碼方案比較簡(jiǎn)單,其量子路徑的解碼結(jié)果可以和Dyson展開(kāi)項(xiàng)保持一致。封閉系統(tǒng)可在Hilbert空間進(jìn)行描述,而開(kāi)放系統(tǒng)則要轉(zhuǎn)換到Liouville空間。此時(shí)環(huán)境作用將同時(shí)出現(xiàn)在演化方程中哈密頓量的對(duì)角元和非對(duì)角元上,常規(guī)的用于封閉系統(tǒng)的編碼方案會(huì)導(dǎo)致量子路徑的解碼結(jié)果與積分的Dyson項(xiàng)結(jié)果不一致。因此,本論文通過(guò)分析與對(duì)比兩種方法路求解徑躍遷幅度的的區(qū)別與聯(lián)系,提出了一套新的哈密頓量編碼方案,能夠巧妙避免哈密度量編碼-觀測(cè)量解碼方法產(chǎn)生的自身到自身的"非物理"躍遷,同時(shí)使得量子路徑的解碼結(jié)果與Dyson項(xiàng)保持精確對(duì)應(yīng)。具體工作如下:1.Lee的八分塊方案能夠優(yōu)化四能級(jí)Rb原子的雙光子吸收強(qiáng)度。分塊的邊界點(diǎn)由一個(gè)多項(xiàng)式方程的根給出。我們把此方法推廣到五能級(jí),同時(shí)也又提出了一種新的全局最優(yōu)的分塊方法,并給出了數(shù)學(xué)上嚴(yán)格的推導(dǎo)和證明。最后把每個(gè)數(shù)值模擬的結(jié)果都與轉(zhuǎn)換極限(TL)脈沖進(jìn)行了對(duì)比,數(shù)據(jù)結(jié)果表明多能級(jí)系統(tǒng)的分塊方案都可以有效的增強(qiáng)雙光子(TPA)路徑振幅。此部分內(nèi)容為第二章。2.對(duì)HE-0D方法在開(kāi)放量子系統(tǒng)中的使用做了進(jìn)一步較為詳細(xì)的討論,而后又從基本的量子力學(xué)出發(fā)計(jì)算路徑幅度。當(dāng)發(fā)現(xiàn)二者有差別的時(shí)候,文中又提出了一些分析和解釋。當(dāng)對(duì)原矩陣的部分對(duì)角線上的元素也進(jìn)行編碼后,二者之間的差別也在逐步縮小。出現(xiàn)了一些發(fā)生在自身能態(tài)中的躍遷能級(jí),可是他們從物理意義上并沒(méi)有相應(yīng)的解釋。此部分內(nèi)容在第三章。3.在本文中出現(xiàn)了一些沒(méi)有實(shí)際物理意義的躍遷,所以接下來(lái)將會(huì)相應(yīng)的提出一些解決方法,由于其數(shù)學(xué)形式比較復(fù)雜,所以首先對(duì)二能級(jí)開(kāi)放量子系統(tǒng)進(jìn)行研究,其中分別分析了極端情況下當(dāng)電場(chǎng)為零的和普遍情況下電場(chǎng)不為零的情況,而且通過(guò)相應(yīng)的數(shù)學(xué)轉(zhuǎn)變,就可以成功的把對(duì)角線元素消除掉,這樣就可以避免了第三章中出現(xiàn)的一些奇怪的躍遷路徑。進(jìn)一步將這種思想拓展到三能級(jí)開(kāi)放量子系統(tǒng)中,也分別做了相應(yīng)的分析和證明,結(jié)果同樣也可以得到與二能級(jí)開(kāi)放量子系統(tǒng)相同的情況。數(shù)值結(jié)果表明HE-OD解碼得到的路徑幅度與Dyson積分結(jié)果一致。此部分內(nèi)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.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O413;O231

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本文編號(hào)：1803402