Extended Wiener-Khinchin theorem for quantum spectral analysis

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.Comment: 13 pages, 5 figure

OCT data for pituitary adenoma eyes

Three-dimensional (3D) spectral-domain optical coherence tomography (SD-OCT) scanning data for pituitary adenoma eyes

OCT data for normal people

Three-dimensional (3D) spectral-domain optical coherence tomography (SD-OCT) for normal eyes

PituitaryAdenomaOCT_Analysis.xlsx

<p>A quantitative investigation of the characteristics presented by three-dimensional (3D) spectral-domain optical coherence tomography (SD-OCT) in pituitary adenoma eyes, using three common indices including thickness, optical intensity ratio, and optical intensity attenuation coefficient (OIAC).</p

ECG’s PPI EMD results.

<p>ECG’s PPI EMD results.</p

Ascertain signal’s PPI EMD results.

<p>Ascertain signal’s PPI EMD results.</p

The relationship between FAR and matching threshold.

<p>The relationship between FAR and matching threshold.</p

An example of fingerprint enhancement and minutiae extraction by P071 method.

<p>(a) Original fingerprint; (b) Enhancement results of (a); (c) Minutiae extraction results of (a).</p

Ascertain signal’s CSI EMD results.

<p>Ascertain signal’s CSI EMD results.</p

ECG’s CSI EMD results.

<p>ECG’s CSI EMD results.</p