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Journal of the Optical Society of America B

Spectral-domain biphoton interferometry with frequency scanning: theoretical proposal and resolution limits

Nikolai A. Ushakov, Маркварт Александр Александрович, Лиокумович Леонид Борисович

Published Sep 27, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.1364/josab.465328

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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.
Biphoton frequency comb (BFC), which encompasses multiple discrete frequency modes and represents high-dimensional frequency entanglement, is crucial in quantum information processing due to its high information capacity and error resilience. It also holds significant potential for enhancing timing precision in quantum metrology. Here, we examine quantum metrology timing limits using the BFC as a probe state and derive a quantum Cramér-Rao bound (QCRB) that depends on the mode number, mode spacing, frequency detuning, and single-mode bandwidth. Our results coincide with previous findings that considered only the latter two factors. Under ideal conditions (zero loss and perfect visibility), this bound can be saturated by both spectrally non-resolved Hong-Ou-Mandel (HOM) interferometry at zero delay and spectrally resolved HOM interferometry at arbitrary delays. In practical scenarios, the Fisher information is below the QCRB but can approach its maximum by increasing the mode number and mode spacing for a fixed delay point, suggesting an optimal strategy for improving the precision of HOM-based sensing in practice. Furthermore, compared to spectrally non-resolved measurement, spectrally resolved measurement is a superior strategy due to its higher Fisher information, shorter measurement times, and ambiguity-free dynamic range.
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 (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.