Study on precision measurement of angular momentum entangled photon states

提出了一种新的轨道角动量纠缠光子测量系统，旨在实现角动量纠缠光子态的精确测量。该系统结合了使用全息图的OAM检测/变换系统、使用干涉仪的叠加态检测系统和通过符合光子计数的量子相关检测。测量目标是参数荧光光子对，并且我们聚焦于包括两个OAM状态的子空间，每个OAM状态用于信号光子和空闲光子。得到以下结果.利用我们的干涉系统对闲频光子进行了量子关联探测，利用传统的全息移位方法对信号光子进行了量子关联探测，成功地证明了OAM纠缠。验证了本系统选择的测量基与传统方法选择的测量基之间的一致性.我们表明，与我们提出的干涉系统，非目标OAM组件的误检测可以减少到0.4%以下的相对检测效率。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度量，并将其作为全息图设计的反馈.阐明了Gouy相位对探测OAM纠缠光子对的影响，提出了一种新的操纵OAM叠加光子态的方法.我们从理论上研究了信号光子和闲频光子的3个或更多OAM态的高维纠缠的产生和检测，考虑了有限晶体长度的影响。我们阐明了高维纠缠对全息移位法得到的符合计数率分布的影响。我们还发现，随着晶体长度的增加，最大符合的位置发生了移动。

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.