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arXiv:2205.11298 · Physical Review Applied

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

Yuanyuan Chen, Lixiang Chen

Published Jul 29, 2022• 9 citations
arXivHTMLPDF

Abstract

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 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.

DOI
10.1103/physrevapplied.18.014077

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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 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.
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.
Precise manipulation of the time–frequency modes of entangled photons is crucial for future quantum science and technologies. Recently, the frequency-domain-quantum-optical-synthesis (FD-QOS) method was demonstrated by creating a superposition of different joint temporal amplitudes: those temporal distributions can be controlled by manipulating the joint spectral amplitude in 2D frequency space via a Fourier optical relation. This FD-QOS method provides an efficient, flexible, and easy-to-control way to precisely modulate the temporal distributions of the entangled photon in an ultrafast region. However, manipulation of only the temporal modes is not sufficient for various applications in quantum information, since spectral modulations are also needed on many occasions. Here, we present a proof-of-concept experiment of two-photon spectral modulation via temporal manipulation of a biphoton wave packet. This protocol, called time-domain-quantum-optical-synthesis (TD-QOS), is achieved by adjusting the relative phases between two joint temporal distributions. In addition, the two-photon joint spectral distributions are characterized by measuring the joint spectral intensities and Hong–Ou–Mandel interferences. The combination of FD-QOS and TD-QOS enables complete control over the biphoton states. Our work would further develop quantum technologies that rely on the time–frequency modes of entangled photons.
Quantum Optical Coherence Tomography (Q-OCT) presents many advantages over its classical counterpart, Optical Coherence Tomography (OCT): it provides an increased axial resolution and is immune to even orders of dispersion. The core of Q-OCT is quantum interference of negatively correlated entangled photon pairs obtained in a Hong-Ou-Mandel configuration. This two-photon interference can be observed in the time domain in the form of dips or in the Fourier domain by means of a joint spectrum. The latter approach proved to be practical in the sense that it alleviated the requirement posed on light in Q-OCT to exhibit strict negative correlations, since the negative correlations can be easily extracted in the Fourier domain as the main diagonal of the joint spectrum. In this work, we investigate the use of this spectral approach in which quantum interference is obtained with classical low-intensity light pulses. We report theoretical calculations and their experimental validation and show that although such classical light is much easier to launch into an experimental system, it offers limited benefits as compared to Q-OCT based on entangled light. We analyse the differences in the characteristics of the joint spectrum obtained with entangled photons and with classical light and explain the origins of these differences.
Hong-Ou-Mandel (HOM) interferometry is a powerful quantum metrology technique to reconstruct the surface-depth profile of transparent samples with complementary benefits of measurement precision and experimental robustness. It is generally assumed that a trade-off exists between the standard HOM interferometry sensitivity and its ambiguity-free dynamic range. Here we challenge this ``well-known'' assumption through the implementation of spectrally resolved HOM interferometry with discrete color entanglement, and show that the well-separated frequencies embedded in a quantum state suffices to achieve great advantages in enhancing the temporal resolution but without limiting its ambiguity-free dynamic range. Backed by the Fisher-information analysis, spectrally resolved coincidence detection is an optimal measurement strategy as it enables us to recover the quantum Cram\'er-Rao bound. These results may significantly facilitate the use of spectrally resolved quantum interference for real-time quantum information processing, such as ultrafast phase transition and spectral-temporal photography.
Abstract Two-photon excitation spectroscopy is a nonlinear technique that has gained rapidly in interest and significance for studying the complex energy-level structure and transition probabilities of materials. While the conventional spectroscopy based on tunable classical light has been long established, quantum light provides an alternative way towards excitation spectroscopy with potential advantages in temporal and spectral resolution, as well as reduced photon fluxes. By using a quantum Fourier transform that connects the sum-frequency intensity and N00N-state temporal interference, we present an approach for quantum interferometric two-photon excitation spectroscopy. Our proposed protocol overcomes the difficulties of engineering two-photon joint spectral intensities and fine-tuned absorption-frequency selection. These results may significantly facilitate the use of quantum interferometric spectroscopy for extracting the information about the electronic structure of the two-photon excited-state manifold of atoms or molecules without any requirement for precise and complicated scanning in the spectral domain. This may be particularly relevant for photon-sensitive biological and chemical samples.
Using spectrally correlated photon pairs instead of classical laser light and coincidence detection instead of light intensity detection, Quantum Optical Coherence Tomography (Q-OCT) outperforms classical OCT in several experimental terms. It provides twice better axial resolution with the same spectral bandwidth and it is immune to even-order chromatic dispersion, including Group Velocity Dispersion responsible for the bulk of axial resolution degradation in the OCT images. Q-OCT has been performed in the time domain configuration, where one line of the two-dimensional image is acquired by axially translating the mirror in the interferometer's reference arm and measuring the coincidence rate of photons arriving at two single-photon-sensitive detectors. Although successful at producing resolution-doubled and dispersion-cancelled images, it is still relatively slow and cannot compete with its classical counterpart. Here, we experimentally demonstrate Q-OCT in a much faster Fourier-domain configuration, theoretically proposed in 2020, where the reference mirror is fixed and the joint spectrum is acquired by inserting long fibre spools in front of the detectors. We propose two joint spectrum pre-processing algorithms, aimed at compensating resolution-degrading effects within the setup. While the first one targets fibre spool dispersion, an effect specific to this configuration, the other one removes the effects leading to the weakening of even-order dispersion cancellation, the latter impossible to be mitigated in the time-domain alternative. Being additionally contrasted with both the time-domain approach and the conventional OCT in terms of axial resolution, imaging range and multilayer-object imaging, Fourier-domain Q-OCT is shown to be a significant step forward towards a practical and competitive solution in the OCT arena.