本文關(guān)鍵詞：拉普拉斯變換在開放量子系統(tǒng)力學(xué)中的應(yīng)用　出處：《吉林大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 開放量子系統(tǒng) 量子相干性 退相干 拉普拉斯變換 開放量子系統(tǒng)動(dòng)力學(xué)

【摘要】：多體開放量子系統(tǒng)的動(dòng)力學(xué)問題是量子信息科學(xué)的一個(gè)研究熱點(diǎn)。一個(gè)開放量子系統(tǒng)的環(huán)境是由無窮多個(gè)自由度組成的熱庫,要精確求解這個(gè)系統(tǒng)的動(dòng)力學(xué)就需要解決含有無窮變量的動(dòng)力學(xué)方程。如果我們將量子系統(tǒng)與其周圍環(huán)境看成一個(gè)大的閉合系統(tǒng),采用薛定諤方程解析其動(dòng)力學(xué),這種方法理論上似乎可行。但是多體開放量子系統(tǒng)薛定諤方程的求解在現(xiàn)有計(jì)算能力下幾乎是辦不到的。因此對(duì)于開放量子系統(tǒng)而言,僅有薛定諤方程本身是遠(yuǎn)遠(yuǎn)不夠的。由于開放量子系統(tǒng)不可避免地會(huì)與周圍環(huán)境自由度發(fā)生相互作用,從而導(dǎo)致量子系統(tǒng)的一部分信息和能量流向環(huán)境。在最初的研究中,人們考慮環(huán)境自由度非常大,系統(tǒng)和環(huán)境之間的耦合非常弱的情況。在這種情況下可以采用玻恩-馬爾可夫近似,系統(tǒng)動(dòng)力學(xué)展現(xiàn)出馬爾可夫特性。但是當(dāng)系統(tǒng)與環(huán)境之間的耦合非常強(qiáng)時(shí),開放量子系統(tǒng)的動(dòng)力學(xué)是非馬爾可夫性的。它流入環(huán)境的信息將在未來的某一時(shí)刻重新對(duì)系統(tǒng)造成影響。本論文在處理馬爾可夫與非馬爾可夫這兩種動(dòng)力學(xué)時(shí),介紹了量子馬爾可夫主方程和非馬爾可夫量子態(tài)擴(kuò)散方程。由于環(huán)境自由度的影響,必然導(dǎo)致量子系統(tǒng)的退相干,這給操控相干量子態(tài)帶來很大困難。目前已有多種方法抑制退相干效應(yīng),本論文介紹動(dòng)力學(xué)解耦調(diào)控法,即通過引入脈沖使得系統(tǒng)與環(huán)境部分解耦。開放量子系統(tǒng)動(dòng)力學(xué)的研究模型在數(shù)學(xué)處理和物理實(shí)現(xiàn)上都是相當(dāng)復(fù)雜的。因此我們需要通過各種數(shù)值計(jì)算或近似技術(shù)實(shí)現(xiàn)對(duì)不相關(guān)變量的約化,進(jìn)而在約化態(tài)空間形成簡(jiǎn)單的描述。一般而言,精確解是探究物理模型的基礎(chǔ),物理模型一旦被精確地解析,它被應(yīng)用到實(shí)驗(yàn)以及其他科研領(lǐng)域的可能性就會(huì)很大,因此我們更希望得到系統(tǒng)動(dòng)力學(xué)的精確解而不是近似解,此時(shí)就要求我們精確求解系統(tǒng)動(dòng)力學(xué)的積分微分方程。數(shù)學(xué)上主要用拉普拉斯變換的方法來求解積分微分方程,本論文主要采用拉普拉斯變換精確求解四個(gè)常用開放量子系統(tǒng)模型的動(dòng)力學(xué)方程:(1)與兩個(gè)環(huán)境相互作用的三能級(jí)原子模型;(2)耗散的JC模型;(3)囚禁在耗散腔里的兩量子比特模型;(4)N量子比特與零溫?zé)釒煜嗷プ饔媚Ｐ�。這四個(gè)物理模型的精確求解表明了拉普拉斯變換法在開放量子系統(tǒng)動(dòng)力學(xué)中的重要地位,也為將來處理更復(fù)雜的動(dòng)力學(xué)方程提供理論依據(jù)和近似求解的基礎(chǔ)。
[Abstract]:The dynamics of multi-body open quantum systems is a hot topic in quantum information science. The environment of an open quantum system is a heat pool composed of infinite degrees of freedom. In order to solve the dynamics of the system accurately, we need to solve the dynamics equation with infinite variables. If we think of the quantum system and its surrounding environment as a large closed system. The Schrodinger equation is used to analyze its dynamics. This method seems to be feasible in theory, but the solution of Schrodinger equation for multibody open quantum system is almost impossible under the existing computational power, so for the open quantum system. The Schrodinger equation alone is far from enough because open quantum systems inevitably interact with the degree of freedom of the surrounding environment. As a result, part of the information and energy of the quantum system flow to the environment. In the initial study, people considered the environment with great degree of freedom. The coupling between the system and the environment is very weak. In this case, the Bosn-Markov approximation can be used, and the dynamics of the system shows the Markov characteristic. But when the coupling between the system and the environment is very strong, the coupling between the system and the environment is very strong. The dynamics of an open quantum system is non-Markov. The information that flows into the environment will re-influence the system at some point in the future. This paper deals with both Markov and non-Markov dynamics. The quantum Markov master equation and the non-Markov quantum state diffusion equation are introduced. Due to the influence of the degree of freedom in the environment, the decoherence of the quantum system is inevitable. This makes it difficult to manipulate coherent quantum states. At present, there are many methods to suppress the decoherence effect. In this paper, the dynamic decoupling control method is introduced. The open quantum system dynamics model is very complicated in mathematical processing and physical implementation. Therefore, we need to use various numerical calculations or approximate techniques. The reduction of uncorrelated variables was achieved by surgery. In general, the exact solution is the basis of exploring the physical model, once the physical model is analyzed accurately. It is very likely that it will be applied to experiments and other fields of scientific research, so we prefer to obtain the exact solution of system dynamics rather than the approximate solution. At this point, we are required to solve the integro-differential equations of system dynamics accurately. In mathematics, the Laplace transformation is mainly used to solve the integrodifferential equations. In this paper, Laplace transform is used to solve the three-level atomic model of interaction between four open quantum system models and two environments. (2) dissipative JC model; (3) two quantum bit models trapped in a dissipative cavity; The exact solution of the four physical models shows the importance of the Laplace transform method in the dynamics of open quantum systems. It also provides the theoretical basis and approximate solution basis for the more complex dynamic equations in the future.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O413

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本文編號(hào)：1418425