光波與物質波的相干態之研究

Abstract

斑圖形成(pattern formation)是在空間或時間上具有某種規律性的非均勻 宏觀結構。它已成為非常多物理、化學、生物各領域研究的課題。研究斑圖 形成的原因及機制，對於揭開自然界形成之謎具有重大意義。在光學斑圖形 成的研究中，奇點光學(singular optics)是研究光波位相奇異性效應的現代物 理光學的新分支。 光場角動量(optical angular momentum)與奇點光學有密不可分的關係。光 子是資訊傳遞的重要載體，透過對光子的能量、線動量和偏振態的分析解碼 可以得到它所攜帶的資訊。光波相干態可由具有明確角動量的態疊加而得 到，所以研究光波相干態的角動量對研究量子糾纏很有幫助。 最近，我們發現氧化式垂直面射型雷射(VCSELs)的高階橫模與二維量子 彈子球檯的波函數機率分佈類似。國際上已逐漸重視此課題，各式各樣的 VCSEL 系統之研究對瞭解介觀量子波函數之物理特徵，有很重要的助益。 近年來，隨著奈米製程技術的不斷提升，對低維半導體結構中的激子 (polariton)的研究已成為凝態物理的研究主題之一。特別是，關於固體中激子 的BEC 現象還有許多爭論，理論方法還在發展中。隨著量子資訊研究熱潮 的興起，人們提出激子可以作為固態量子資訊的載體之一，低維半導體中激 子BEC 提供了固態量子資訊處理的理想基態。 本計畫將以超大口徑固態微片雷射與半導體微型雷射研究各式各樣的斑 圖形成，重點放在spiral、linked、knotted 的斑圖形成，並研究所產生的雷射 光波之奇點特性。利用簡併雷射共振腔產生具有超大角動量的光波相干態， 並研究其基本物理特性，用以提供自旋與軌道耦合效應的重要參考基礎。另 一方向是研究半導體激子的相干態之物理特性，利用奈秒高尖峰功率的Q 開 關固態雷射激發週期性量子井得到超高激子密度，進而研究半導體中的激子 相變與超流現象。

Natural pattern formation possesses some common features that make it possible to understand the analogies in different fields. In the optical pattern formation, the phase singularities or the optical vortices reveal the interesting phase structures but also signify the existence of the local angular momentum (AM). So far, only Laguerre-Gaussian laser modes have been confirmed to have a well-defined orbital AM and applied to the fields of fundamental researches and practical applications such as optical tweezers, optical traps, and wireless and optical communications. Recently, we have shown that the transverse modes of vertical-cavity surface-emitting lasers (VCSELs) are equivalent to the wave functions in the quantum billiards with the shapes the same as the lateral confinements of VCSELs and can be directly observed. The scars and superscars have been observed in chaotic and square shaped VCSELs respectively but the observation of superscars in other shaped VCSELs is still absent. On the other hand, there is significant recent interest in the study of exciton polaritons which are composite 2D weakly interacting bosons in semiconductor microcavities. In constrast to the exciton BEC, the condensate of polartions can be achieved at much higher temperature because their effective mass is as small as 10-4 of the mass of an electron. From the theoretical point of view, cavity polaritons in the quasithermal equilibrium regime are expected to give rise to a Kosterlitz-Thouless (KT) phase transition toward superfluidity. However, no experimental signature for polariton superfluidity has been reported until now. In this proposal, we will (1) explore the pattern formation of linked and knotted optical waves, (2) investigate the angular momentum density of generalized coherent states, (3) fabricate other shaped VCSELs with large apertures and observe the near-field transverse patterns of the VCSELs at near threshold currents, (4) achieve a room-temperature high-density polariton condensate in a periodic quantum-well structure by intense nonresonant optical excitation.