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Quantitative Phase Imaging

Dual wavelength Hong-Ou-Mandel imaging

Ashley Lyons, Khales Kassem, Daniele Faccio, Jack Radford

Published Mar 12, 2024• 0 citations
Publisher

Abstract

Hong-Ou-Mandel (HOM) interferometry, manifesting as photon bunching at a beamsplitter, can provide high precision optical path length sensing yet is robust to phase noise and immune to phase-wrapping. In this work we demonstrate how the sensitivity of HOM based imaging can be enhanced using dual wavelength illumination whilst maintaining its high level of robustness. We observe a beating in the second order correlation function due to the interference between the two wavelengths bands with a periodicity determined by the wavelength separation. These small-scale features can be used to precisely determine optical path length at the nanometre scale whilst a coarse (micron scale) estimation can be obtained by measuring only one of the bands.

DOI
10.1117/12.3009777

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Hong-Ou-Mandel (HOM) interferometry, manifesting as photon bunching at a beamsplitter, can provide high precision optical path length sensing yet is robust to phase noise and immune to phase-wrapping. In this work we demonstrate how the sensitivity of HOM based imaging can be enhanced using dual wavelength illumination whilst maintaining its high level of robustness. We observe a beating in the second order correlation function due to the interference between the two wavelengths bands with a periodicity determined by the wavelength separation. These small-scale features can be used to precisely determine optical path length at the nanometre scale whilst a coarse (micron scale) estimation can be obtained by measuring only one of the bands.
Hong-Ou-Mandel (HOM) interference, i.e. the bunching of indistinguishable photons at a beam splitter is a staple of quantum optics and lies at the heart of many quantum sensing approaches and recent optical quantum computers. Although originally proposed as a method for sensing micron-scale variations in photon propagation path lengths and despite the detection of photon bunching using camera technologies, the technique is still to be extended to the imaging domain. We report a full-field, scan-free, quantum imaging technique that exploits HOM interference to reconstruct the surface depth profile of transparent samples. We measure both the bunched and anti-bunched photon-pair distributions at the HOM interferometer output which are combined to provide a lower-noise image of the sample. This approach demonstrates the possibility of HOM microscopy as a tool for label-free imaging of transparent samples in the very low photon regime.
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).
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.
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.
The quantum interference of two wavelength-entangled photons overlapping at a beamsplitter results in an oscillating interference pattern. The frequency of the beat note is dependent on the wavelength separation of the entangled photons but is robust to wavelength scale perturbations that can limit the practicality of standard interferometry. Here we use two-colour entanglement interferometry to evaluate the variation in thickness of a semi-transparent sample in combination with two-dimensional raster scanning. The axial precision and the dynamic range of the microscope are actively controlled by adjusting the wavelength separation of the entangled photon pairs. Sub-μmμmμm precision is reported using up to 12.3 nm12.3~nm12.3 nm of detuning and ∼104\sim10^4∼104 detected photon pairs.