Quantum Wiener-Khinchin Theorem for Spectral-Domain Optical Coherence Tomography

The 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 the Wiener-Khinchin theorem that provides a translation between time-energy degrees of freedom of biphoton wave function 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 frequencyentangled 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.

Automated summary

This paper explores the application of the quantum Wiener-Khinchin theorem in describing the correlation between the joint spectral intensity and temporal signal of biphoton. The experimental demonstration using spectrally resolved detection in frequency-entangled two-photon Hong-Ou-Mandel interference shows the effectiveness of the quantum Wiener-Khinchin theorem. The results suggest that this method can achieve high measurement precision and time capturing ability in spectral-domain quantum optical coherence tomography, providing advantages over conventional HOM interferometric schemes.