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Optics Letters

Subattosecond x-ray Hong–Ou–Mandel metrology

Sergey Volkovich, S. Shwartz

Published Apr 3, 2020• 10 citations
Publisher

Abstract

We show that subattosecond delays and subangstrom optical path differences can be measured by using Hong-Ou-Mandel interference measurements with x-rays. Our scheme relies on the subattosecond correlation time of photon pairs that are generated by x-ray spontaneous parametric down-conversion, which leads to a dip in correlation measurements with a comparable width. Therefore, the precision of the measurements is expected to be better than 0.1 attosecond. We anticipate that the scheme we describe in this work will lead to the development of various techniques of quantum measurements with ultra-high precision at x-ray wavelengths.

DOI
10.1364/ol.382044

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We show that subattosecond delays and subangstrom optical path differences can be measured by using Hong-Ou-Mandel interference measurements with x-rays. Our scheme relies on the subattosecond correlation time of photon pairs that are generated by x-ray spontaneous parametric down-conversion, which leads to a dip in correlation measurements with a comparable width. Therefore, the precision of the measurements is expected to be better than 0.1 attosecond. We anticipate that the scheme we describe in this work will lead to the development of various techniques of quantum measurements with ultra-high precision at x-ray wavelengths.
We show that sub-attosecond delays and sub-Angstrom optical path differences can be measured by using Hong-Ou-Mandel interference measurements with x-rays. We propose to use a system comprising a source based on spontaneous parametric down-conversion for the generation of broadband x-ray photon pairs and a multilayer-based interferometer. The correlation time of the photon pairs and the Hong-Ou-Mandel dip are shorter than 1 attosecond, hence the precision of the measurements is expected to be better than 0.1 attosecond. We anticipate that the scheme we describe in this work will lead to the development of various techniques of quantum measurements with ultra-high precision at x-ray wavelengths.
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.
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.
Sub-μm\mu\mathrm{m}μm Axial Precision Depth Imaging with Entangled Two-Colour Hong-Ou-Mandel Microscopy
Hong-Ou-Mandel (HOM) interference results in a modified probability of bunching events when indistinguishable photons with a relative timing offset interact at a beamsplitter. Lyons et al. recently achieved attosecond precision in time delay measurement by applying a classical Fisher information analysis to HOM interference [1]. More recently an increase in the measurement precision has been shown by detuning the central wavelengths of the signal and idler from an entangled two-colour photon pair source and applied in temperature drift detection for optical fibres [2]. Here we exploit the timing resolution of the HOM interference to implement a robust 3D imaging microscope with tuneable sensitivity from millimetre to sub-micrometre.
Quantum technologies have been widely recognized as unprecedented opportunities for ultra-high precision metrology. As a celebrated example in modern quantum optics, the Hong-Ou-Mandel (HOM) interferometer is well-known for enabling temporal resolutions on the attosecond scale. However, the relatively low Fisher information per trial in ordinary HOM measurements typically necessitates tens of thousands of repetitions to achieve such precision. Here, we propose and demonstrate a sample-half-inserted HOM (SHOM) interferometer, which enhances the Fisher information by five orders of magnitude in a single interference event. By introducing an asymmetric photon-sample interaction, the SHOM configuration produces a distinctive dip-bump-dip interference structure, converting what was previously viewed as an artifact into a helpful metrological resource. Experimentally, we measured the optical path difference with an average precision of 4.09 nm (13.63 as) and an average accuracy of 1.22 nm (4.07 as) using O(107)O(10^7)O(107) photons. Our results establish SHOM interferometry as an efficient phase-insensitive approach, not only paving the way toward practical quantum-enhanced thickness measurement for transparent materials, but also serving as an elegant strategy to improve the performance of various quantum devices.
Quantum interference forces two indistinguishable input photons to depart a beamsplitter in the same (of two possible) spatial output modes; this is known as the Hong-Ou-Mandel (HOM) effect. It provides a quantitative way of measuring the distinguishability between two photons and also has been utilised to determine their relative temporal delays [1, 2]. HOM interferometry offers numerous advantages over its classical counterpart, most importantly it lacks any dependence on the phase of the photons and therefore can potentially provide reliable measurements in environments where the phase is unstable. To date there have been very few investigations on the precision that is achievable with HOM interferometry. Experiments with collinear geometries have yielded sensitivities as low as 0.1fs however these approaches are limited to measurements of birefringence and other polarisation dependent effects [3, 4], as the precision derives from the inherently stable shared path of the photon pairs. Typical non-shared path HOM interferometers exhibit resolution of roughly 1–3 fs (0.3–1 μm).