| 摘要: | 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. |
