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arXiv:2110.03564 · Journal of Modern Optics

Spectral single photons characterization using generalized Hong–Ou–Mandel interferometry

Nicolas Fabre

Published May 10, 2022• 9 citations
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Abstract

We propose new methods to characterize the spectral-temporal distribution of single photons. The presented protocols take advantage of spectral filtering, frequency entanglement between two single photons, the one of interest and a reference, followed by the generalized Hong–Ou–Mandel interferometer. The measurement of the coincidence probability in these different schemes reveals the chronocyclic Wigner distribution, the pseudo-Wigner one and the spectrogram at the single photon level.

DOI
10.1080/09500340.2022.2073613

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We propose new methods to characterize the spectral-temporal distribution of single photons. The presented protocols take advantage of spectral filtering, frequency entanglement between two single photons, the one of interest and a reference, followed by the generalized Hong–Ou–Mandel interferometer. The measurement of the coincidence probability in these different schemes reveals the chronocyclic Wigner distribution, the pseudo-Wigner one and the spectrogram at the single photon level.
Hong-Ou-Mandel interferometry takes advantage of the quantum nature of two-photon interference to increase the resolution of precision measurements of time delays. Relying on few-photon probe states, this approach is applicable also in cases of extremely sensible samples and it achieves attosecond-scale resolution, which is relevant to cell biology and two-dimensional materials. Here, we theoretically analyze how the precision of Hong-Ou-Mandel interferometers can be significantly improved by engineering the spectral distribution of two-photon probe states. In particular, we assess the metrological power of different classes of biphoton states with non-Gaussian time-frequency spectral distributions, considering the estimation of both time and frequency shifts. We find that grid states, characterized by a periodic structure of peaks in the chronocyclic Wigner function, can outperform standard biphoton states in sensing applications [1].
The Hong-Ou-Mandel interferometer is a versatile tool for analyzing the joint properties of photon pairs, relying on a truly quantum interference effect between two-photon probability amplitudes. While the theory behind this form of two-photon interferometry is well established, the development of advanced photon sources and exotic two-photon states has highlighted the importance of quantifying precisely what information can and cannot be inferred from features in a Hong-Ou-Mandel interference trace. Here we examine Hong-Ou-Mandel interference with regard to a particular class of states, so-called quantum frequency combs, and place special emphasis on the role spectral phase plays in these measurements. We find that this form of two-photon interferometry is insensitive to the relative phase between different comb line pairs. This is true even when different comb line pairs are mutually coherent at the input of a Hong-Ou-Mandel interferometer and the fringe patterns display sharp temporal features. Consequently, Hong-Ou-Mandel interference cannot speak to the presence of high-dimensional frequency-bin entanglement in two-photon quantum frequency combs.
Hong-Ou-Mandel interferometry takes advantage of the quantum nature of two-photon interference to increase the resolution of precision measurements of time-delays. Relying on few-photon probe states, this approach is applicable also in cases of extremely sensible samples and it achieves attosecond (nanometer path length) scale resolution, which is relevant to cell biology and two-dimensional materials. Here, we theoretically analyze how the precision of Hong-Ou-Mandel interferometers can be significantly improved by engineering the spectral distribution of two-photon probe states. In particular, we assess the metrological power of different classes of biphoton states with non-Gaussian time-frequency spectral distributions, considering the estimation of both time-and frequency-shifts. We find that grid states, characterized by a periodic structure of peaks in the chronocyclic Wigner function, can outperform standard biphoton states in sensing applications. The considered states can be feasibly produced with atomic photon sources, bulk non-linear crystals and integrated photonic waveguide devices.
We propose theoretically a quantum interferometer in which the NOON state interferometer is combined with the Hong-Ou-Mandel interferometer. With this interferometer, the temporal interference patterns associated with biphoton frequency sum and difference can be shown in different parts of a single interferogram. It is thus possible to simultaneously obtain the spectral correlation information of biphotons in both frequency sum and difference by taking the Fourier transform from such an interferogram. This provides a method for complete spectral characterization of an arbitrary two-photon state with exchange symmetry and might be useful in quantum Fourier-transform spectroscopy where direct spectral measurement is difficult. Furthermore, as it can realize the measurement of time intervals on three scales at the same time, we expect that it can provide a method in quantum metrology. Finally, we discuss another potential application of such an interferometer in the generation and characterization of high-dimensional and phase-controlled frequency entanglement.
The paper proposes a spectral-domain version of a biphoton (Hong–Ou–Mandel) interferometry. The operation principle is based on measuring the coincidence rate of entangled photons while scanning the difference between their central frequencies. A theoretical apparatus describing the operation principle and the resolution limits of the proposed spectral-domain biphoton interferometry is developed. The analysis is based on quantum and classical Cramer–Rao bounds. It was shown that the proposed spectral-domain biphoton interferometry approach enables the mitigation of the fringe number counting errors, often encountered in classical spectral interferometry. A comparison with a conventional Hong–Ou–Mandel biphoton interferometry is also presented.