Quantum Wiener-Khinchin theorem for spectral-domain optical coherence tomography

TL;DR

This paper introduces a quantum Wiener-Khinchin theorem (QWKT) linking two-photon spectral and temporal correlations, experimentally demonstrating its application in spectral-domain quantum optical coherence tomography to improve measurement precision.

Contribution

The paper presents the first experimental demonstration of QWKT and applies it to enhance spectral-domain quantum optical coherence tomography.

Findings

QWKT connects two-photon spectral intensity and temporal cross-correlation via Fourier transform.

Application of QWKT improves measurement precision in quantum optical coherence tomography.

QWKT facilitates advancements in quantum information processing and interferometric spectroscopy.

Abstract

Wiener-Khinchin theorem, the fact that the autocorrelation function of a time process has a spectral decomposition given by its power spectrum intensity, can be used in many disciplines. However, the applications based on a quantum counterpart of Wiener-Khinchin theorem that provides a translation between time-energy degrees of freedom of biphoton wavefunction still remains relatively unexplored. Here, we use a quantum Wiener-Khinchin theorem (QWKT) to state that two-photon joint spectral intensity and the cross-correlation of two-photon temporal signal can be connected by making a Fourier transform. The mathematically-defined QWKT is experimentally demonstrated in frequency-entangled two-photon Hong-Ou-Mandel (HOM) interference with the assistance of spectrally-resolved detection. We apply this method to spectral-domain quantum optical coherence tomography that detects thickness-induced optical delays in a transparent sample, and show that our method suffices to achieve great advantages in measurement precision within a wide dynamic range and capturing time over the conventional HOM interferometric schemes. These results may significantly facilitate the use of QWKT for quantum information processing and quantum interferometric spectroscopy.