對光束量角的特性描述: 有幾何相位的鬼成像和攜帶分數值軌道角動量的光束

Characterizing the Angular Quantity of an Optical Beam:Ghost Imaging Involving Berry Phase and Optical Beams Carrying Fractional Orbital Angular Momentum

黃孝智(Huang, Hsiao-Chih)

指導教授 ： 石明豐

國立臺灣大學/理學院/物理研究所/博士(2012年)

https://doi.org/10.6342/NTU.2012.10550

摘要

在光學的領域裡，量子糾纏實驗的蓬勃發展是由把晶體中自發性參數向下轉換(SPDC)當成糾纏光子源開始的。從光子線動量的糾纏，量子鬼成像(QGI)是對物體沒有作直接空間解析的偵測，但卻對與其相關的光束作關聯測量，而可得的影像[1, 2]。此偵測為本著對光子對的二階關聯測量。在以往人們也可以對光強度的相干性作二階關聯測量[3]，這個將糾纏光子源改為熱光源的鬼成像則被稱為熱鬼成像(TGI) [4, 5]。
光可以有軌道角動量(OAM)是與其相波前的分布有關的[6]。如同其糾纏，SPDC光子對的OAM是守恆的[7]。另一方面，Berry相位[8]，又名為幾何相位，在量子干涉實驗中有重要的角色，是得於一個系統在經由在漢米頓參數空間的封閉路徑。本博士論文中，Berry相位如同在QGI的光束中的角位移，可由“同時測量”來顯示。
有著螺旋波前相位的光被稱作旋渦光束(VLB)。帶有整數值OAM的VLB，其等相位面處處都是連續的，然而，假如這螺旋相位對其光軸轉一圈的變化不為2π的整數倍[9]，將會有一條斷線出現在光影像上，且此VLB的每顆光子OAM的期望值會是分數值[10]。因為其組成模態有各自的 Guoy相位，故這分數值的VLB在自由空間的傳播是不穩定的[11, 12]。
本論文的架構鋪成如下。第一章是對所有背景知識的介紹。在第二章，我們呈現了帶有Berry相位的QGI的結果，由此觀念，我們可用光子角位置來傳送多位元的訊息。在第三章，我們論證了一個沒有任何特徵的圓形光束，可以用TGI測量出其旋轉的角度，這可以是一個在沒有時間上或空間上對光波做調變的新方法來傳送訊息。在第四章，我們設計了一套干涉方法，來測量非相干或相干混和的分數值VLB。第五章是總結和未來工作。

關鍵字

軌道角動量 ； 糾纏光子對 ； 鬼成像

並列摘要

In the field of optics, the experimental development of quantum entanglement started prospering since the utilization of the spontaneous parametric down conversion (SPDC) as the entangled photon source. Utilizing entanglement in photon linear momentum, quantum ghost imaging (QGI) [1, 2] can obtain the image of an object, which is not on the path of the signal light beam to the “scanning” detector (camera) but on the path of its entangled idler counterpart detected by a “bucket” detector without any spatial resolution. This detection is essentially the second-order correlation measurement executed at the level of a pair of photons. Classically, one can also measure the second-order correlation [3] as the intensity interference, which allows one to replace the entangled photon source by thermal light to perform the thermal ghost imaging (TGI) [4, 5].
Light can carry orbital angular momentum (OAM) associated with its wavefront distribution [6]. The OAM of the SPDC photon pair are conserved as well as entangled [7]. On the other hand, Berry phase [8], the geometric phase acquired by a system after following a closed circuit in Hamiltonian parameter space, plays a major role in many experiments related to quantum interference. In this dissertation, Berry phase is introduced into the signal light beam of the QGI as the angular displacement, and to be revealed by the coincident (second-order correlation) detection.
Light beams with helical wavefronts are called vortex light beams (VLB). For a VLB with integral OAM, the wave function and its derivative are continuous everywhere. However, if the phase to go around its center is not an multiple of 2π [9], there will be a branch line and this VLB carries an expectation value of fractional OAM per photon [10]. The fractional VLB is not stable as propagating in the free space [9] because its composite modes have different Guoy phases [11, 12].
This dissertation is organized in the following way. Chapter 1 is an introduction to the background knowledge. In Chapter 2, we present the results of QGI with Berry phase, which can enable us to transmit multi-bit information by the photon orbital angular position. In Chapter 3, we demonstrate that the rotation angle of a featureless round light beam can be measured by TGI, and this opens a new way to send information without modulating the carrier wave temporally or spatially. In Chapter 4, we design an interferometric method to measure fractional topological charges of incoherent or coherent vortex light beams. Chapter 5 is the summary and future works.

並列關鍵字

OAM ； entangled photon pairs ； ghost imaging

參考文獻

[90] 陳國祥, 攜帶貝里相位的量子影像, in: 物理研究所, 國立臺灣大學, 2008.

[34] 陳宣槐, Separation of Hermite-Gaussian laser modes, in: 物理研究所, 國立臺灣大學, Taipei, 2007.

[37] 林彥廷, 測量漩渦光的分數值軌道角動量之理論分析, in: 物理研究所, 國立臺灣大學, Taipei, 2010.

[51] P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, P.H. Eberhard, Phys Rev A, 60 (1999) R773-R776.

[119] L.E.E. de Araujo, M.E. Anderson, Opt Lett, 36 (2011) 787-789.