两个任意非相干点光源的量子极限超分辨：战胜 Rayleigh 魔咒的复苏
Quantum-limited superresolution of two arbitrary incoherent point sources: beating the resurgence of Rayleigh's curse
AI总结：
本文研究未知且不等光子数下两个任意非相干点光源的量子极限超分辨，给出光子数接近条件、不同区间精度及点扩散函数差异的影响。
摘要：
超分辨已被证明能够克服 Rayleigh 判据的限制，并在分辨两个非相干光学点光源间距时显著提升精度。然而，近年来人们发现，如果两个非相干光源的光子数未知，而两者的实际光子数并不相同，超分辨的精度优势就会消失。在本工作中，我们首先详细分析两个具有相同点扩散函数的非相干光源之间间距的估计精度，并表明当两个光源的光子数不同但足够接近时，仍可实现超分辨，只是精度有所不同。我们找到了为实现超分辨两个光源的光子数需要接近到何种程度的条件，并推导了在光子数差的不同区间内超分辨的精度。我们进一步考虑两个具有不同点扩散函数的非相干光源的超分辨问题，表明光子数差异、两个点扩散函数之间的差异以及两个光源间距之间的竞争决定了超分辨的精度。所得结果展现出不同于两个点光源具有相同点扩散函数且光子数相等情形的精度极限，并扩展了量子超分辨技术可实现的参数区间。最后，我们利用 Gaussian 点扩散函数对这些结果进行了说明。
英文摘要：
Abstract Superresolution has been demonstrated to overcome the limitation of the Rayleigh's criterion and achieve significant improvement of the precision in resolving the separation of two incoherent optical point sources. However, in recent years, it was found that if the photon numbers of the two incoherent optical sources are unknown, the precision of superresolution vanishes when the two photon numbers are actually different. In this work, we first analyze the estimation precision of the separation between two incoherent optical sources with the same point-spread functions in detail, and show that when the photon numbers of the two optical sources are different but sufficiently close, the superresolution can still realized but with different precisions. We find the condition on how close the photon numbers of two optical sources need to be to realize the superresolution, and derive the precision of superresolution in different regimes of the photon number difference. We further consider the superresolution for two incoherent optical sources with different point-spread functions, and show that the competition between the difference of photon numbers, the difference of the two point-spread functions and the separation of the two optical sources determines the precision of superresolution. The results exhibit precision limits distinct from the case of two point sources with identical point-spread functions and equal photon numbers, and extend the realizable regimes of the quantum superresolution technique. The results are finally illustrated by Gaussian point-spread functions.
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