EAGER: Smart single-pixel quantum statistical imaging beyond the Abbe-Rayleigh criterion

光子作为一种很有前途的信息源的识别引发了各种量子光子技术，用于从信息处理到成像的多种目的。近年来，利用光场的量子特性来克服衍射的可能性已经成为量子成像的主要目标之一。人们对量子光学超分辨率的兴趣在于它有可能改善现有的远程成像和显微镜方案的性能。有趣的是，为经典超分辨率成像奠定基础的开创性工作在2014年获得了诺贝尔化学奖。这些基本贡献证明了进行超出阿贝-瑞利分辨率标准的成像的可能性。最近，量子光学领域的研究人员进行了一些实验，旨在通过将目标物体投影到空间模式来提高经典成像方案的空间分辨率。这些传统的协议依赖于一系列空间投影测量来提取相位信息，然后使用这些信息来提高光学系统的空间分辨率。不幸的是，这些方案需要关于光束相干特性的先验信息，以及严格的对准条件。这项研究计划的目的是证明，可以通过测量光子的量子统计性质来克服光学仪器有限的空间分辨率，因为光子对衍射不敏感。光的量子属性的识别将使用人工神经网络进行。该计划的成功完成将使远程成像和超分辨率显微镜技术成为可能。这个项目的教育目标是通过吸引学生进行超分辨率成像的研究，并在路易斯安那州的阿森松教区图书馆为普通观众开发一系列讲座和演示，为包容和公平的科学传播做出贡献。该项目包括一系列理论和实验里程碑。这项研究计划的理论部分旨在开发新的形式来模拟多粒子系统量子相干性的演化。这些物理系统导致了在O(2nn！)量级上的计算困难问题，其中n表示成像系统中的光子数。该计划的实验部分将在桌面光学装置中进行。研究人员将制备具有可调相干特性和不可分辨程度的多个光源，这些光束将通过光子数分辨检测来表征。这些能力将使该团队能够1)开发量子相干的一般理论来描述任意数量的光源组合产生的光子统计数据，2)设计人工神经网络来演示具有光子数分辨率的单像素相机，以及3)实验演示任意数量的光子发射器和散射器的单像素超分辨率成像。这些里程碑的完成将导致第一个超分辨率单像素相机家族，这些相机利用人工智能的自学习功能来识别真正未知的光源混合的统计波动。这些新型光子器件的潜力将在远程成像和显微镜的背景下进行探索。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The identification of the photon as a promising information resource has triggered a variety of quantum photonic technologies for multiple purposes that range from information processing to imaging. Recently, the possibility of using the quantum properties of the light field to overcome diffraction has become one of the main goals of quantum imaging. The interest in quantum optical superresolution resides in its potential for improving the performance of existing schemes for remote imaging and microscopy. Interestingly, seminal work that established the foundations of classical superresolution imaging was awarded with the Nobel Prize of Chemistry in 2014. These fundamental contributions demonstrated the possibility of performing imaging beyond the Abbe-Rayleigh resolution criterion. Recently, researchers from the quantum optics community have conducted experiments that aim to boost spatial resolution of classical schemes for imaging by projecting target objects onto spatial modes. These conventional protocols rely on a series of spatial projective measurements to pick up phase information that is then used to boost the spatial resolution of optical systems. Unfortunately, these schemes require a priori information regarding the coherence properties of the light beams, a well as stringent alignment conditions. The purpose of this research program is to demonstrate that the limited spatial resolution of optical instruments can be overcome through measurements of the quantum statistical properties of photons, which are insensitive to diffraction. The identification of the quantum properties of light will be performed using artificial neural networks. The successful completion of the program will enable transformative technology for remote imaging and superresolving microscopy. The educational objectives of this project are to contribute to the inclusive and fair diffusion of science by engaging students to perform research on superresolving imaging, and by developing a series of lectures and demonstrations for general audiences in the Ascension Parish Library from Louisiana.This program includes a series of theoretical and experimental milestones. The theoretical component of this research program aims to develop new formalisms to model the evolution of the properties of quantum coherence of multiparticle systems. These physical systems lead to computationally hard problems scaling on the order of O(2nn!), where n represents the number of photons in the imaging system. The experimental part of the program will be carried out in table-top optical setups. The investigators will prepare multiple light sources with tunable coherence properties and degrees of indistinguishability, these beams will be characterized through photon-number-resolving detection. These capabilities will enable the team to 1) develop a general theory of quantum coherence to describe the photon statistics produced by the combination of an arbitrary number of light sources, 2) design artificial neural networks to demonstrate single-pixel cameras with photon-number resolution, and 3) experimentally demonstrate single-pixel superresolution imaging of an arbitrary number of photon emitters and scatterers. The completion of these milestones will lead to the first family of superresolving single-pixel cameras that exploit the self-learning features of artificial intelligence to identify the statistical fluctuations of truly unknown mixtures of light sources. The potential of these novel photonic devices will be explored in the context of remote imaging and microscopy.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.