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Sensors

Photon Phase Delay Sensing with Sub-Attosecond Uncertainty

Fabrizio Sgobba, Andrea Andrisani, Luigi Santamaria Amato

Published Mar 29, 2024• 4 citations
Publisher

Abstract

The application of statistical estimation theory to Hong-Ou-Mandel interferometry led to enticing results in terms of the detection limit for photon reciprocal delay and polarisation measurement. In the following paper, a fully fibre-coupled setup operating in the telecom wavelength region proves to achieve, for the first time, in common-path Hong-Ou-Mandel-based interferometry, a detection limit for photon phase delay at the zeptosecond scale. The experimental results are then framed in a theoretical model by calculating the Cramer-Rao bound (CRB) and, after comparison with the obtained experimental results, it is shown that our setup attains the optimal measurement, nearly saturating CRB.

DOI
10.3390/s24072202

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The application of statistical estimation theory to Hong-Ou-Mandel interferometry led to enticing results in terms of the detection limit for photon reciprocal delay and polarisation measurement. In the following paper, a fully fibre-coupled setup operating in the telecom wavelength region proves to achieve, for the first time, in common-path Hong-Ou-Mandel-based interferometry, a detection limit for photon phase delay at the zeptosecond scale. The experimental results are then framed in a theoretical model by calculating the Cramer-Rao bound (CRB) and, after comparison with the obtained experimental results, it is shown that our setup attains the optimal measurement, nearly saturating CRB.
The use of statistical estimation theory to boost the metrological performance of the measurement apparatus is becoming increasingly popular in a wide range of applications. Recently, such an approach has been adopted in Hong Ou Mandel interferometry, setting a new record in time delay and polarization measurement. Here, we extend these pioneering experiments in the telecom range to unlock the full potential of the information-based approach combined with a versatile spectral range, aiming for its adoption in fiber-coupled devices of up to hundreds of kilometers long as bobines or optical networks. Our measurement saturates the Cramér-Rao bound and in a long lasting experiment returns an Allan deviation of the polarization angle of 0.002 degs in 1 h of integration time.
Hong-Ou-Mandel (HOM) interferometry enables delay estimation at the quantum precision limit but is traditionally constrained to path differences within the coherence time of the interfering photons. Here, we demonstrate single-measurement path-delay sensing at the measurement Cramer-Rao bound using spectrally resolved HOM interference, thereby removing the conventional dynamic-range limitation imposed by the photon coherence window, with no scanning required for calibration. By extracting delay information from the spectral interference fringes of spectrally entangled photon pairs, we retain near-optimal sensitivity over an operational range exceeding the photon coherence time by over two orders of magnitude. Using one million detected photon pairs, we achieve a time-delay precision of 20 attosecond (6 nm), while real-time operation (at 1 Hz) yields 330 attosecond (100 nm) precision. Because the estimator relies on fringe periodicity rather than absolute coincidence rates, the method is intrinsically robust to photon losses and variations in interference visibility, eliminating the need for recalibration. As a practical demonstration, we measure the thickness of a 300 um transmissive target with nanometer-scale precision. These results mark a significant step towards deploying quantum-limited measurements in real-world sensing applications using HOM interferometry.
Traditional Hong-Ou-Mandel (HOM) interferometry, insensitive to photons phase mismatch, proved to be a rugged single-photon interferometric technique. By introducing a post-beam splitter polarization-dependent delay, it is possible to recover phase-sensitive fringes, obtaining a temporal quantum eraser that maintains the ruggedness of the original HOM with enhanced sensitivity. This setup shows promising applications in biological sensing and optical metrology, where high sensitivity requirements are coupled with the necessity to keep light intensity as low as possible to avoid power-induced degradation. In this paper, we developed a highly sensitive single photon birefringence-induced delay sensor operating in the telecom range (1550 nm). By using a temporal quantum eraser based on common path Hongr-Ou-Mandel Interferometry, we were able to achieve a sensitivity of 4 as for an integration time of 2·104 s.
We provide a statistically robust and accurate framework to measure and track the polarisation state of light employing Hong-Ou-Mandel interference. This is achieved by combining the concepts of maximum likelihood estimation and Fisher information applied to photon detection events. Such an approach ensures that the Cramér-Rao bound is saturated and changes to the polarisation state are established in an optimal manner. Using this method, we show that changes in the linear polarisation state can be measured with 0.6 arcminute precision (0.01 degrees).
When two indistinguishable photons are each incident on separate input ports of a beamsplitter, they "bunch" deterministically, exiting via the same port as a direct consequence of their bosonic nature. This two-photon interference effect has long-held the potential for application in precision measurement of time delays, such as those induced by transparent specimens with unknown thickness profiles. However, the technique has never achieved resolutions significantly better than the few-femtosecond (micrometer) scale other than in a common-path geometry that severely limits applications. We develop the precision of Hong-Ou-Mandel interferometry toward the ultimate limits dictated by statistical estimation theory, achieving few-attosecond (or nanometer path length) scale resolutions in a dual-arm geometry, thus providing access to length scales pertinent to cell biology and monoatomic layer two-dimensional materials.