Study on precision measurement of angular momentum entangled photon states

为了实现轨道角动量纠缠光子态的精确测量，提出了一种新的轨道角动量纠缠光子态测量系统。该系统结合了基于全息图的OAM检测/变换系统、基于干涉仪的叠加态检测系统和基于重合光子计数的量子相关检测系统。测量目标是参数化荧光光子对，我们将重点放在由信号光子和空闲光子的两个OAM状态组成的子空间上。得到了以下结果：利用我们的干涉系统对空闲光子进行了量子相关检测实验，对信号光子进行了传统的全息图移位方法，成功地显示了OAM纠缠。证实了干涉测量系统选择的测量基与常规方法选择的测量基的一致性。我们发现，使用我们提出的干涉系统，非靶向OAM成分的误检率可以降低到0.4%以下，相对检测效率。这是对传统方法的明显改进。我们通过改进全息图和光轴对准来改进我们的系统。定义了一种新的全息图畸变的定量测量方法，并将其作为全息图设计的反馈。阐明了Gouy相位在OAM纠缠光子对探测中的作用，提出了一种新的方法来操纵OAM叠加光子态。考虑到有限晶体长度的影响，我们从理论上研究了信号光子和空闲光子涉及3个或更多OAM态的高维纠缠的产生和检测。阐明了高维纠缠对全息图移位法得到的符合计数率分布的影响。我们还发现，最大重合点的位置随晶体长度的增加而变化。

We proposed a new measurement system for photons entangled in orbital angular momentum (OAM), with the aim to carry out precision measurement of angular momentum entangled photon states. The system combines an OAM detection/transformation system using hologram, a superposition state detection system using interferometer, and quantum correlation detection by coincidence photon counting. The measurement targets were parametric fluorescence photon pairs, and we focused on a subspace comprising two OAM states each for the signal and idler photons. The following results were obtained.1. A quantum correlation detection experiment using our interferometric system for the idler photon and the conventional hologram shifting method for the signal photon successfully showed OAM entanglement. Correspondence between the measurement basis chosen by our interferometric system and that chosen by the conventional method was confrmed.2. We showed that with our proposed interferometric system, misdetection of untargeted OAM components can be reduced to below 0.4% in terms of relative detection efficiency. This is a clear improvement over the conventional method.3. We refined our system by improving the holograms and optical axis alignment. A new quantitative measure of hologram distortion was defined and used as a feedback to the hologram design.4. We clarified the effect of Gouy phase in detection of OAM entangled photon pairs, and proposed a new method to manipulate OAM superposition photon states.5. We examined theoretically the generation and detection of higher dimensional entanglement involving 3 or more OAM states for both the signal and idler photons, taking into consideration effect of finite crystal length. We clarified the effect of higher dimensional entanglement on coincidence count rate distribution obtained by the hologram shifting method. We also found that the position of maximum coincidence shifts with the increase of crystal length.