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Optical and Quantum Sensing and Precision Metrology II

Real-time displacement measurement with the ultimate quantum precision through spectrally resolved two-photon interference

Yingwen Zhang, Duncan G. England, Vincenzo Tamma, Ebrahim Karimi, Benjamin Sussman

Published Mar 5, 2026• 0 citations
Publisher

Abstract

We demonstrate real-time displacement measurement using spectrally resolved Hong–Ou–Mandel (HOM) interference that saturates the quantum Cram´er-Rao bound. Unlike conventional HOM-based methods, our approach does not require the displacement to be confined within the HOM dip width, typically a few tens of microns. By analyzing the periodicity of spectral interference fringes, we can maintain sensitivity at the quantum limit over displacement ranges extending to hundreds of microns. In principle, the measurable range can be extended up to the coherence length of the pump laser, limited only by the spectral resolution of the detector. We further demonstrate that real-time displacement tracking is feasible with current technology, establishing this technique as a practical and powerful tool for quantum-enhanced sensing and metrology.

DOI
10.1117/12.3080991

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We demonstrate real-time displacement measurement using spectrally resolved Hong–Ou–Mandel (HOM) interference that saturates the quantum Cram´er-Rao bound. Unlike conventional HOM-based methods, our approach does not require the displacement to be confined within the HOM dip width, typically a few tens of microns. By analyzing the periodicity of spectral interference fringes, we can maintain sensitivity at the quantum limit over displacement ranges extending to hundreds of microns. In principle, the measurable range can be extended up to the coherence length of the pump laser, limited only by the spectral resolution of the detector. We further demonstrate that real-time displacement tracking is feasible with current technology, establishing this technique as a practical and powerful tool for quantum-enhanced sensing and metrology.
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.
Two-photon interference, commonly known as Hong-Ou-Mandel (HOM) interference [1] , has attracted a great deal of interest in quantum sensing, including the precision timing measurements [2] and quantum optical coherence tomography [3] . While the dip of the HOM interference is the direct measure of the purity of the single-photon, the width of the HOM dip relates to the coherence time of the interfering photons. The broad consensus for using the HOM interferometer for sensing application remained the HOM dip width as the limiting factor for the precision measurements. As a consequence, the ultra-broadband photon sources have long been hailed as a vital prerequisite for ultra-precise HOM interferometry. Here, we have studied the variation in the width of the HOM dip with the crystal length for the continuous-wave pump laser and measured the HOM dip as low as 8.2 ± 0.2 µm corresponding to the spectral width of the single-photon source of 79.6±1.9 nm useful for sensitive sensing applications.
Abstract Hong–Ou–Mandel (HOM) interference, bunching of two indistinguishable photons on a balanced beam‐splitter, has emerged as a promising tool for quantum sensing. There is a need for wide spectral‐bandwidth photon pairs (for high‐resolution sensing) with high brightness (for fast sensing). Here, the generation of photon‐pairs with flexible spectral‐bandwidth even using single‐frequency, continuous‐wave diode laser enabling high‐precision, real‐time sensing is showed. Using 1‐mm‐long periodically‐poled KTP crystal, degenerate, photon‐pairs with spectral‐bandwidth of 163.42±1.68 nm are produced resulting in a HOM‐dip width of 4.01±0.04 m to measure a displacement of 60 nm, and sufficiently high brightness to enable the measurement of vibrations with amplitude of 205 ± 0.75 nm and frequency of 8 Hz. Fisher‐information (FI) and maximum likelihood estimation enables optical delay measurements as small as 4.97 nm with precision (Cramér–Rao bound) and accuracy of 0.89 and 0.54 nm, respectively, therefore showing HOM sensing capability for real‐time, precision‐augmented, in‐field quantum sensing applications.
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.
Extracting information from a fast-moving object plays a crucial role in better understanding natural phenomena and exploring the unknown world. The conventional Hong-Ou-Mandel (HOM) sensor can acquire temporal information of an object using the single-shot method. However, this method is strictly limited by the temporal resolution of coincidence detection. On the other hand, implementing a suitable quantum interferometer for tracking fast-moving objects with relatively little technological effort has long been sought after, particularly for photon-sensitive biological and chemical dynamic processes. Here, we present a fast HOM interferometer based on quantum interference on a biphoton beat note and spectrally resolved detection. To verify the feasibility of our method, we demonstrate a proof-of-principle experiment that implements a fast HOM sensor for observing the track of a moving translation stage. These results may facilitate the use of quantum interference for enhancing the temporal resolution and processing speed in a fast HOM-based sensor, which has an important scientific significance in both fundamental research and applied science.
Hong-Ou-Mandel (HOM) interference is an intrinsic quantum phenomena that goes beyond the possibilities of classical physics, and enables various applications in quantum metrology. While the timing resolution of HOM-based sensor is generally investigated, the ultimate quantum sensitivity in the estimation of transverse deflection or displacement between paired photons interfering at a balanced beam splitter has been explored relatively little. Here, we present an experimental demonstration of a spatial HOM interferometry for measuring the transverse deflection of an optical beam by using transverse momentum sampling measurements. This feasible scheme suffices to achieve great precision with comparatively little technological effort, which circumvents the stringent requirement in direct imaging resolution at the diffraction limit. We can adaptively determine optimum working points using a Fisher information analysis, and demonstrate an optimized spatial HOM interferometry according to practical applications. These results may significantly facilitate the use of quantum interference for high precision spatial sensing, and pave the way to more complex quantum imaging techniques like nanoscopic microscopy.