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原子在光子晶體中的幅射現象研究

程思誠

Published Aug 1, 2009• 0 citations
OpenAlex

Abstract

[[abstract]]吾人已應用分數微積分法於具有長時間記憶現象的光子晶體系統，利用分數微積分法研究在光子晶體中的原子幅射現象，吾人可容易獲得正確且無多值函數的物理解，光子在光子晶體中多次散射所引起的碎形現象，可由分數微積分所得之分數微分方程式正確描述。由於分數微積分法的容易性，因此吾人計畫第一年研究如何將分數微積分法擴大應用於三階原子在光子晶體中的幅射現象，兩高能階與低能階經由光子晶體偶合而形成幅射干涉，此干涉現象將影響原子激發態的機率分佈，此兩激發態間的同調性可產生量子拍節，至於第二年的研究吾人將分數微積分法應用於不穩定系統中的Zeno 與反Zeno 效應，觀測次數的多寡可影響幅射的快慢，對於三階原子在光子晶體中的幅射干涉現象，觀測次數的多寡亦可影響干涉現象，進而影響兩激發態間的同調性，最後第三年的研究吾人將考慮單原子在光子晶體缺陷中的幅射現象，缺陷中的光子可與原子強力作用產生分裂的光子與原子混合態(拉比分裂)，此混合態與光子晶體儲庫間的作用產生有別於光子晶體中的原子幅射現象合，混合態間的同調性可產生量子拍節。 We applied the fractional calculus to study the dynamics of the spontaneous emission of an atom in a photonic crystal band gap (PBG). Contrary to the previous study, we show that there is no unphysical state of fractionalized atomic population in the excited state when the resonant atomic frequency lies outside the band gap. Therefore, we believe that the correct description of the dynamics of the spontaneous emission in a PBG should be expressed in terms of the fractional calculus.We apply the fractional calculus to study the quantum interference of spontaneous emission from a three-level atom with the two upper levels coupled to the photonic crystal reservoir (the first-year proposal), Quantum Zeno and anti-Zeno effect of an atom embedded in photonic crystals (the second-year proposal), and the spontaneous emission of an atom in a defect of a PBG. (the third-year proposal). It has been shown that there exists a dressed state of the atom with a localized field mode. Such a dressed photonic effect will be used to study the effect of quantum interference without a coherent driving field in the spontaneous emission of a three-level atom embedded in a photonic crystal. The atom has two upper levels and one lower level. The two upper levels are coupled to the lower one via the same reservoir. The interference between two transitions leads to quasiperiodic oscillations of population between the two upper levels with large amplitudes.We shall study how frequent measurement on a three-level atom embedded in PBG can affect the quantum interference. If a small disorder or defect is introduced into the photonic crystal, there exists an ultimate photonic nanocavity, with ultra-large quality factor Q factor. There is a strong coupling between light and an atom. The spontaneous emission spectrum will consist of a doublet (Rabi splitting). The coherence of a doublet can create quantum beats. Quantum beats do indeed occur even if the system is not initially prepared in a coherent superposition of the upper states, when multiple scattering events are taken into account.

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[[abstract]]吾人已應用分數微積分法於具有長時間記憶現象的光子晶體系統，利用分數微積分法研究在光子晶體中的原子幅射現象，吾人可容易獲得正確且無多值函數的物理解，光子在光子晶體中多次散射所引起的碎形現象，可由分數微積分所得之分數微分方程式正確描述。由於分數微積分法的容易性，因此吾人計畫第一年研究如何將分數微積分法擴大應用於三階原子在光子晶體中的幅射現象，兩高能階與低能階經由光子晶體偶合而形成幅射干涉，此干涉現象將影響原子激發態的機率分佈，此兩激發態間的同調性可產生量子拍節，至於第二年的研究吾人將分數微積分法應用於不穩定系統中的Zeno 與反Zeno 效應，觀測次數的多寡可影響幅射的快慢，對於三階原子在光子晶體中的幅射干涉現象，觀測次數的多寡亦可影響干涉現象，進而影響兩激發態間的同調性，最後第三年的研究吾人將考慮單原子在光子晶體缺陷中的幅射現象，缺陷中的光子可與原子強力作用產生分裂的光子與原子混合態(拉比分裂)，此混合態與光子晶體儲庫間的作用產生有別於光子晶體中的原子幅射現象合，混合態間的同調性可產生量子拍節。 We applied the fractional calculus to study the dynamics of the spontaneous emission of an atom in a photonic crystal band gap (PBG). Contrary to the previous study, we show that there is no unphysical state of fractionalized atomic population in the excited state when the resonant atomic frequency lies outside the band gap. Therefore, we believe that the correct description of the dynamics of the spontaneous emission in a PBG should be expressed in terms of the fractional calculus.We apply the fractional calculus to study the quantum interference of spontaneous emission from a three-level atom with the two upper levels coupled to the photonic crystal reservoir (the first-year proposal), Quantum Zeno and anti-Zeno effect of an atom embedded in photonic crystals (the second-year proposal), and the spontaneous emission of an atom in a defect of a PBG. (the third-year proposal). It has been shown that there exists a dressed state of the atom with a localized field mode. Such a dressed photonic effect will be used to study the effect of quantum interference without a coherent driving field in the spontaneous emission of a three-level atom embedded in a photonic crystal. The atom has two upper levels and one lower level. The two upper levels are coupled to the lower one via the same reservoir. The interference between two transitions leads to quasiperiodic oscillations of population between the two upper levels with large amplitudes.We shall study how frequent measurement on a three-level atom embedded in PBG can affect the quantum interference. If a small disorder or defect is introduced into the photonic crystal, there exists an ultimate photonic nanocavity, with ultra-large quality factor Q factor. There is a strong coupling between light and an atom. The spontaneous emission spectrum will consist of a doublet (Rabi splitting). The coherence of a doublet can create quantum beats. Quantum beats do indeed occur even if the system is not initially prepared in a coherent superposition of the upper states, when multiple scattering events are taken into account.
The two models of three-level (one upper level and two lower levels, or two upper levels and one lower level) atom embedded in a double-band photonic crystal are adopted. The atomic transitions from the upper levels to the lower levels are assumed to be coupled by the same reservoir which are respectively the isotropic photonic band gap (PBG) modes, the anisotropic PBG modes and the free vacuum modes. The effects of the fine structure of the atomic ground state levels in the model with one upper level and two lower levels and the quantum interferences in the model with two upper levels and one lower level on the spontaneous emission spectrum of an atom are investigated in detail. Most interestingly, it is shown that new spontaneous emission lines are produced from the fine splitting of atomic ground state levels in the isotropic PBG case. The quantum interferences induce additional narrow spontaneous lines near the transition from the empty upper level to the lower level.
众所周知,传统定义的单模相位算符不是幺正算符。我们选择另一种定义相算符的途径,鉴于相位的测量总是相对的,就像势能的测量是相对于零势能位置一样,所以我们在双模空间中引入相位算符。具体做法是在纠缠态表象的基础上提出幺正的双模相位算符,它的本征值就是经典位相。在此理论框架内,相角对应的正则共轭算符是光子数差算符。并且给出了数差-相测不准关系以及此相位算符的Weyl-Wigner经典对应,发现它是双变数相空间(q1,p1;q2,p2)中的相exp［iargtanp1+p1q1-q2］。
The impacts of an external driving field on the spontaneous emission from an excited two-level atom embedded in a double-band photonic crystal is investigated. In the upper level coupling, a dark line occurs, which stems from deductive quantum interference induced by the external driving field. The dark line appears with an additional peak when it is outside the band gap of the PBG reservoirs. The dark line cannot be seen when it falls into the band gap. In the case of lower level coupling, interference plays no role. The emission spectrum displays two incoherent modified Lorentzian lines that have two singularities in each side of the band gap in isotropic PBG reservoirs.
我们介绍“进 anatom 的密度矩阵方程的条款在 photonic 乐队差距(PBG ) 嵌入的腐烂率”水库成功地。由利用 masterequations，探查吸收系列和在 thePBG 水库的一个三水平的原子的折射度性质被获得。在象原子的吸收上的干扰也被拿了进 account.It 的量的 theeffects 一样的原子和 PBG 水库之间的相互作用有趣在一分散的折射度 areexhibited 的异常分散关系的二种不同类型排队。这里使用的方法论能被用于在一座 PBG 水库嵌入的另外的原子模型的量干扰效果的 theoreticalinvestigation。
Генерация фотона возбужденным атомом происходит в конечном по времени процессе перестройки внутренних полей напряжений вокруг электрона, меняющего орбиту. Излучение света имеет близкие аналогии с генерацией вихревых структур в сплошной среде и адекватно отражается в рамках традиционной, не квантовой механики. Рассмотрены силовые параметры перехода электрона между термами атома в режиме автоколебаний с излучением фотона. Проведен анализ трансформации исходного момента вращения электрона в спин излучаемого фотона с формированием нового момента вращения за счет работы поля ядра. Из частотных и энергетических зависимостей получены оценки геометрических размеров оптического фотона. The generation of a photon by an excited atom occurs in a fi nite time-dependent process of rearrangement of internal stress fi elds around an electron that changes its orbit. Radiation of light has close analogies with the generation of vortex structures in a continuous medium and is adequately refl ected in the framework of traditional, non-quantum mechanics. Power, energy characteristics of the electron transition between the terms of the atom in the regime of self-oscillations with the emission of a photon are considered. An analysis is made of the transformation of the initial angular momentum of the electron into the spin of the emitted photon with the formation of a new angular momentum due to the work of the nuclear fi eld. From the frequency and energy dependences, estimates of the geometric dimensions of the optical photon are obtained.
The coherent control of cooperative spontaneous emission from two identical non-overlapping three-level atoms in the V-configuration located within a photonic band gap (PBG) material with two resonant frequencies near the upper band edge of the PBG and confined to a region small in comparison to their radiation wavelengths but still greater than their atomic sizes is investigated. The dependencies of cooperative effects in which a photon emitted by one atom is reabsorbed by the other atom on the inter-atomic separation, on the initial state of the two-atom system, on the strength of the driving control laser field, and on the detuning of the atomic resonant frequencies from the upper band edge frequency is analyzed so as to identify the conditions for which these cooperative effects are enhanced or inhibited. Cooperative effects between atoms are shown to be influenced more by the PBG than by the nature of the atomic transitions involved. Excited state populations as well as coherences between excited levels are expressed in terms of time-dependent amplitudes which are shown to satisfy coupled integro-differential equations for which analytic solutions are derived under special conditions. Unlike for the case of one atom in a PBG where the fractional non-zero steady state populations on the excited levels as well as the coherence between the excited levels are constants independent of time, in the case of two atoms in PBG these quantities continuously oscillate as a manifestation of beating due to the continuous exchange between the two atoms of the photon trapped by the PBG. The values of these quantities as well as the amplitudes and frequencies of their oscillations depend of the parameters of the system, providing different ways of manipulating the system. The general formalism presented here is shown to recapture the special results of investigations of similar systems in free space when the non-Markovian memory kernels of the PBG are replaced by delta function dependent Markovian memory kernels.