測量漩渦光的分數值軌道角動量之理論分析

Abstract

光子除了可以攜帶和偏振方向有關的自旋角動量，亦可以攜帶和橫向相位分布有關的軌道角動量。由於光子的偏振方向可由二維空間來描述，因此可以實現量子資訊理論裡的「量子二位元」。另一方面，光子的橫向正交模態則具有無窮多維，故可用來實現「量子多位元」。實驗上，可使用電腦全像片、空間光調製器以及螺旋相位片來產生帶有軌道角動量的漩渦光。 僅管近軸電磁波方程式的本徵函數「拉蓋爾高斯模態」只帶有整數型的軌道角動量，但可藉由在光束的徑向引入直線式的相位不連續奇異，進而產生每顆光子軌道角動量期望值為非整數的漩渦光。本論文藉由串接多個馬赫任德干涉儀，可直接量測分數型漩渦光的拓樸荷，並進而求得其內光子攜帶的軌道角動量期望值。

Photons can have both spin angular momentum (SAM) and orbital angular momentum (OAM). The former is associated with the polarization of light beams, and the latter is associated with the transverse phase distribution of light beams. Because the polarization states of light beams can be described by a two-dimensional Hilbert space, the SAM states can be used to realize the qubit in the quantum information theory. On the other hand, the spatial transverse basis is infinite-dimensional and therefore can constitute the qunit system. In experiment, the vortex beams carrying OAM can be generated by computer-generated holograms, spiral phase plates or spatial light modulators. Although the Laguerre-Gaussian modes, which are the eigenfunctions of the paraxial wave equation, contain only integer-value OAM, one can introduce radial phase discontinuity on the beam profile to generate vortex beams with photons carrying fractional OAM expectation values. By cascading several Mach-Zehnder interferometers in this thesis, we can measure the topological charge of the fractional vortex beams directly and recognize the OAM expectation values of the photons.