量子相干性論文：單量子體系的相干性及光子統(tǒng)計研究

1、量子相干性論文：單量子體系的相干性及光子統(tǒng)計研究【中文摘要】光與物質(zhì)的相互作用是現(xiàn)代原子分子光物理和量子控制等的重要研究內(nèi)容。以激光、激光制冷、原子力探針掃描儀等為標(biāo)志的實驗技術(shù),以及以玻色-愛因斯坦凝聚、電磁誘導(dǎo)透明等為代表的光-物質(zhì)相干現(xiàn)象使量子力學(xué)的研究深入到了納米尺度和單量子體系,這不僅突破了系綜平均的局限,同時在理論上激發(fā)了對量子開放體系的研究。目前,諸多理論方法被發(fā)展出來,包括量子主方程(master equation)>量子跳躍(quantum jump)、量子軌線(quantum trajectory)、相容歷史(consistent history)、量子測量理論(如K

2、raus representation)等。量子相干性被認為是量子體系的關(guān)鍵性質(zhì),不同的相干性導(dǎo)致了很多新奇的量子效應(yīng),比如電子雙縫干涉、糾纏光子、量子霍爾效應(yīng)等。自發(fā)輻射誘導(dǎo)相干性是一種由自發(fā)輻射系數(shù)所導(dǎo)致的相干性,在原子相干性研究中占有重要的地位。在光-物質(zhì)體系中,光場和物質(zhì)都具有相干性,且二者具有統(tǒng)一的基礎(chǔ)。為了同時描述物質(zhì)(原子、分子、量子點等)和光場的相干性,通過引入密度矩陣所對應(yīng)的特征函數(shù),光子的量子統(tǒng)計效應(yīng)以及各高階統(tǒng)計量等就可以被描述。在本論文中,我們采用產(chǎn)生函數(shù)方法研究光與物質(zhì)的相互作用體系的相干性和光子統(tǒng)計性質(zhì)。我們討論了被廣泛研究的包括砷化鎵量子點(GaAs)和銣原子(R

3、b)在內(nèi)的單量子體系的相干性,并討論了相關(guān)實驗驗證。在第一章,我們介紹了單量子體系相干性的和發(fā)展歷史,在單量子尺度上的精確控制已成為現(xiàn)代量子理論和量子技術(shù)的核心。我們討論了一些常見的重要的原子相干現(xiàn)象,包括量子拍、相干粒子數(shù)囚禁等；在理論上,我們簡要介紹了幾種可以用來描述光子相干性和統(tǒng)計的方法。在第二章,我們介紹了量子開放體系的理論基礎(chǔ)。我們首先討論了密度矩陣和相關(guān)的特征函數(shù)以及分布函數(shù)等的性質(zhì)。然后,我們討論了體系演化的Liouville方程、Lindblad方程、Kraus表象理論以及光-物質(zhì)相互作用體系的產(chǎn)生函數(shù)方程,并介紹了高階統(tǒng)計量。在第三章,我們集中研究了自發(fā)輻射誘導(dǎo)相干(SGC)

4、。首先,我們介紹了SGC的物理基礎(chǔ)和相關(guān),比如暗共振、自發(fā)輻射消減以及自發(fā)輻射相干的模擬方法等。然后,我們詳細討論了單量子多能級體系中的量子拍現(xiàn)象,以及V型三能級體系在脈沖激發(fā)下和超精細三能級體系在連續(xù)場驅(qū)動下的性質(zhì)。在第四章,我們研究了四能級體系中的電磁誘導(dǎo)透明現(xiàn)象(EIT)和SGC效應(yīng)。我們介紹了EIT的相關(guān)效應(yīng),包括光速減緩、光放大、多透明窗等,以及EIT的理論基礎(chǔ),包括暗極化子和去退相干子空間(DFS)理論。然后,我們在失諧空間中分析了雙型四能級體系的EIT結(jié)構(gòu)和Mandels Q參量所反映的光子統(tǒng)計性質(zhì)。研究表明,SGC效應(yīng)可以導(dǎo)致一種真空協(xié)助透明現(xiàn)象,我們詳細分析了其動力學(xué)機制。在

5、第五章,我們研究了N型四能級體系中的巨克爾效應(yīng)和SGC效應(yīng)。同樣,我們首先介紹了GKE的理論基礎(chǔ)和相關(guān)應(yīng)用,諸如量子邏輯門、光學(xué)開關(guān)等。然后,我們討論了外加控制場和開關(guān)場對非線性克爾吸收和AT (Autler-Townes)分裂的控制。我們發(fā)現(xiàn),SGC效應(yīng)可以導(dǎo)致非線性克爾吸收的消失,這說明體系中暗態(tài)可以被SGC所恢復(fù)。另外,我們還討論了光學(xué)開關(guān)過程中對應(yīng)的光子反聚束效應(yīng)。在第六章,我們給出簡要的總結(jié)和展望。在展望中,我們主要討論了SGC效應(yīng)在最近的一些發(fā)展、糾纏光子對的統(tǒng)計性質(zhì)、不同能級結(jié)構(gòu)中的原子相干性以及產(chǎn)生函數(shù)方法的應(yīng)用與推廣。在第七章附錄中,我們介紹了所用到的銣原子的能級結(jié)構(gòu),以及對

6、主方程的檢驗規(guī)則?！居⑽恼縏he light-matter interaction is one of the central topics of modern atomic, molecular, and optical physics (AMO) and quantum control. The experimental technology as laser, laser cooling, and atomic force probe scanner etc, as well as the quantum interference phenomenon like Bose-Einst

7、ein condensate (BEC) and electromagnetically induced transparency (EIT) etc greatly improved the Quan-tum Mechanics to the nano-scale and single quantum system, which brought up new theoretical research trends by disregarding former methods like the ensemble-averaging. At present, the theories, incl

8、ude the quantum master equation, quantum jump, quantum trajectory, consistent history, Kraus representation etc, are devel-oping. The key feature of the quantum system and behavior is represented by the quantum coherence, for which there exist many kinds causing various processes, such as the double

9、-slit interference of electrons, entangled photons, quantum hall effect etc. The spontaneously generated coherence (SGC) is the coherence caused by the spontaneous emission in vacuum, which is crucial in the atomic coherence scope. The light field also the matter, like atom, molecule, quantum dots,

10、in the light-matter system both have coherence, with one unique foundation indeed. To describe the coherence of them at the same time, one of the effective method is the generating function (characteristic function) corresponding to the density matrix, from which the quantum behavior of photon stati

11、stics and higher-order counting moments can be captured.In this thesis, we investigate the quantum coherence and statistics of photon emission in the light-matter interaction system via the generating function (GF). Particularly, we focus on the dynamics of the widely concerned quantum dots like GaA

12、s and Rb atom driven by laser field, as well as the realization of some processes in experiment.In Chapter 1, we introduce the background of the quantum coherence of light-matter interaction system and the history of its development. The concrete control on single quantum system scale has become the

13、 focus of modern quantum theory and technology. We discuss some primary phenomenon of atomic coherence, like quantum beats, coherent population trapping etc. We also describe several theories on photon statistics including the GF approach.In Chapter 2, we introduce the theoretical foundation of the

14、quantum open system. Firstly, we introduce the methods of density matrix, characteristic & dis-tribution functions also the quantum coherence functions. Then we focus on the dynamics of the density matrix (wave function), described by the Liouville equa-tion, Lindblad equation, Kraus sum-operato

15、r representation, also we deduce the GF equations for the light-matter system, and the related observable of photon statistics.In Chapter 3, we study the spontaneously generated coherence (SGC). In the first part, we discuss the physical background of SGC and some notable effects, including dark sta

16、te, spontaneous emission cancellation, also the simulation of SGC etc. Next, we focus on the quantum beats in the quantum multi-level system, the photon emission behavior driven by pulses in V-type system, and also the splitting of the dark state in fine-splitting V-type system.In Chapter 4, we stud

17、y the electromagnetically induced transparency (EIT) and the SGC effects. We describe the related processes, like slow light, gain without inversion, multi-transparency windows etc, and the theoretical generalization in-cluding the dark-state polariton theory and decoherence-free subspace (DFS). In

18、the detuning space, we further investigate the EIT in the double A-type system via the single Rb atom. Due to the effects of SGC, the vacuum-assisted transparency (VAT) can be induced beyond the ability of EIT. We also study the SGC effects on Mandels Q parameter.In Chapter 5, we study the giant Ker

19、r effects (GKE) and the SGC effects. We firstly introduce the foundation of GKE and related applications mainly in quantum information and computation, like the quantum phase gate, optical switching etc. In N-type system, we study the control of nonlinear Kerr absorption and AT splitting. We find th

20、at the GKE can be eliminated by the effects of SGC, and the dark state revival is predicted. As well, we point out that the photon statistics manifests anti-bunching during the photon switching.In Chapter 6, we conclude and discuss the further potential topics, such as the SGC effects on entanglemen

21、t in recent research, the relation between statistics and entanglement, the atomic coherence in various systems, also the development of the GF approach.In Chapter 7, we introduce the energy structure of the 87Rb atom employed in this thesis, and the rules of master equation in case of problems of its complexity.【關(guān)鍵詞】量子相干性 光子統(tǒng)計 產(chǎn)生函數(shù)【英文關(guān)鍵詞】quantum coherence photon statistic generating function【目錄】單量子體系的相干性及光子統(tǒng)計研究摘要8-10Abstract10-12符號說明13-14第一章 緒論14-22§1.1 研究背景14-16§1.2 原子相干現(xiàn)象16-18§1.3 光子統(tǒng)計方法18-20&