Extended Wiener-Khinchin theorem for quantum spectral analysis

TL;DR

This paper extends the classical Wiener-Khinchin theorem to a quantum version using biphoton interferometry, enabling spectral analysis of quantum light through time-domain measurements, with experimental verification.

Contribution

The authors develop and experimentally verify a quantum Wiener-Khinchin theorem that links biphoton spectral information to time-domain quantum interference patterns.

Findings

Extended WKT connects biphoton spectral distributions to Fourier transforms of quantum interference patterns.

Experimental validation conducted using Mach-Zehnder, Hong-Ou-Mandel, and NOON interferometers.

The theorem enables quantum spectral analysis from time-domain measurements, advancing quantum spectroscopy.

Abstract

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.