We demonstrate spectroscopy of incoherent light with sub-diffraction resolution. In a proof-of-principle experiment we analyze the spectrum of a pair of incoherent point-like sources whose separation is below the diffraction limit. The two sources mimic a planetary system, with a brighter source for the star and a dimmer one for the planet. Acquiring spectral information about the secondary source is hard because the two images have a substantial overlap. This limitation is solved by leveraging a structured measurement based on spatial-mode demultiplexing, where light is first sorted in its Hermite-Gaussian components in the transverse field, then measured by photon detection. This allows us to effectively decouple the photons coming from the two sources. An application is suggested to enhance exoplanets' atmosphere spectroscopy. A number of experiments of super-resolution imaging based on spatial demultiplexing have been conducted in the past few years, with promising results. Here, for the first time to the best of our knowledge, we extend this concept to the domain of spectroscopy.
The University of Queensland（昆士兰大学）；ARC Centre of Excellence in Quantum Biotechnology（量子生物技术卓越中心）；Queensland Brain Institute（昆士兰大脑研究所）；RMIT University（皇家墨尔本理工大学）；University of Otago（奥塔哥大学）
Conservative classical and quantum resolution limits for incoherent imaging
从极大极小参数估计的角度，提出了两个非相干点光源的统计分辨率的经典极限和量子极限。与早期的结果的基础上的Cramér-Rao界，这里提出的限制，基于最坏情况下的误差准则和贝叶斯版本的Cramér-Rao界，是有效的任何有偏或无偏估计，并服从光子数标度，是符合实际的估计行为。这些结果证明，从极大极小的角度来看，Tsang，Nair和Lu最近提出的空间模式解复用（SPADE）测量方案[Phys. Rev. X 6，031033（2016）]仍然优于足够高光子数的直接成像。
Passive optical superresolution at the quantum limit
University of Oxford（牛津大学）；RTX BBN Technologies（RTX BBN技术公司）；University of Maryland, College Park（马里兰大学帕克分校）；National University of Singapore（新加坡国立大学）；University of Nottingham（诺丁汉大学）；Sorbonne Université（索邦大学）
