The classical Wiener–Khinchin theorem (WKT), which can extract spectral information by classical interferometers through Fourier transform, is a fundamental theorem used in many disciplines. However, there is still a need for a quantum version of WKT, which could connect correlated biphoton spectral information by quantum interferometers. Here, we extend the classical WKT to its quantum counterpart [i.e., extended WKT (e-WKT)], which is based on two-photon quantum interferometry. According to the e-WKT, the difference–frequency distribution of the biphoton wavefunctions can be extracted by applying a Fourier transform on the time-domain Hong–Ou–Mandel interference (HOMI) patterns, while the sum-frequency distribution can be extracted by applying a Fourier transform on the time-domain NOON state interference (NOONI) patterns. We also experimentally verified the WKT and e-WKT in a Mach–Zehnder interference (MZI), a HOMI, and a NOONI. This theorem can be directly applied to quantum spectroscopy, where the spectral correlation information of biphotons can be obtained from time-domain quantum interferences by Fourier transform. This may open a new path for the study of light–matter interaction at the single photon level.

中文翻译：

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扩展的Wiener–Khinchin定理用于量子光谱分析

可以通过经典干涉仪通过傅立叶变换提取光谱信息的经典维纳-欣钦定理（WKT）是许多学科中使用的基本定理。但是，仍然需要一种量子形式的WKT，它可以通过量子干涉仪连接相关的双光子光谱信息。在这里，我们将经典的WKT扩展到基于双光子量子干涉法的量子对应物（即扩展的WKT（e-WKT））。根据e-WKT，可以通过对时域Hong-Ou-Mandel干扰（HOMI）模式应用傅里叶变换来提取双光子波函数的频差分布，而总和频率分布可以通过以下方法提取：对时域NOON状态干扰（NOONI）模式应用傅里叶变换。我们还通过马赫-曾德尔干涉（MZI），HOMI和NOONI对WKT和e-WKT进行了实验验证。该定理可直接应用于量子光谱，其中双光子的光谱相关信息可通过傅立叶变换从时域量子干涉中获得。这可能为研究单光子水平的光-质相互作用开辟新的途径。