量子谱分析的推广Wiener-Khinchin定理
Extended Wiener-Khinchin theorem for quantum spectral analysis
摘要：
经典的维纳-欣钦定理（Wiener-Khinchin theorem，WKT）是一个应用于多个学科的基本定理，它可以利用经典干涉仪通过傅里叶变换提取光谱信息。然而，仍然需要量子版本的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扩展到它的量子对应物，即，扩展的WKT（e-WKT），它是基于双光子量子干涉。根据e-WKT，双光子波函数的差频分布可以通过对时域Hong-Ou-Mandel干涉（HOMI）图案应用傅立叶变换来提取，而和频分布可以通过对时域NOONI干涉（NOONI）图案应用傅立叶变换来提取。我们还在马赫-曾德尔干涉（MZI），HOMI和NOONI中实验验证了WKT和e-WKT。该定理可直接应用于量子光谱学，即通过傅里叶变换从时域量子干涉中获得双光子的光谱相关信息。这可能为在单光子水平上研究光与物质的相互作用开辟一条新的途径。
英文摘要：
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 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 pathway for the study of light-matter interaction at the single photon level.
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