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arXiv:2609.12786

Spatial symmetry in few-photon interference and quantum metrology

Éloi Descamps, Pérola Milman

quant-phSubmitted Sep 11, 2026• Announced Sep 14, 2026• 0 citations
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Abstract

In previous work [Physical Review Letters, 136(6):060807, 2026], we developed a symmetry-based framework for generalized Hong-Ou-Mandel interference and its applications to quantum metrology. Here, we apply this framework to experimentally accessible configurations involving a few photons and explore how it sheds new light on a variety of existing results while suggesting new experimental perspectives. We first reinterpret a two-photon Mach-Zehnder interferometer as a generalized Hong-Ou-Mandel experiment and show how its photon-counting statistics and metrological performance follow from the spatial symmetry of an effective probe state. We then study two coherently pumped parametric photon-pair sources, derive their complete output distribution, and connect source indistinguishability with spatial symmetry. Finally, we extend the discussion to a three-mode interferometer and show that the same symmetry principles provide a natural description of three-photon interference in tritter configurations.

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23 pages, 5 figures

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In previous work [Physical Review Letters, 136(6):060807, 2026], we developed a symmetry-based framework for generalized Hong-Ou-Mandel interference and its applications to quantum metrology. Here, we apply this framework to experimentally accessible configurations involving a few photons and explore how it sheds new light on a variety of existing results while suggesting new experimental perspectives. We first reinterpret a two-photon Mach-Zehnder interferometer as a generalized Hong-Ou-Mandel experiment and show how its photon-counting statistics and metrological performance follow from the spatial symmetry of an effective probe state. We then study two coherently pumped parametric photon-pair sources, derive their complete output distribution, and connect source indistinguishability with spatial symmetry. Finally, we extend the discussion to a three-mode interferometer and show that the same symmetry principles provide a natural description of three-photon interference in tritter configurations.
The Hong-Ou-Mandel interferometer is a foundational tool in quantum optics with both fundamental and practical significance. Earlier works identified that input-state symmetry under exchange of the two spatial modes is fundamental in the understanding of the Hong-Ou-Mandel effect. We now show that this notion of symmetry is central to generalizing this effect. In particular, this point of view enables the construction of extensions beyond the standard two single-photon case to arbitrary input states, as well as to configurations with more than two spatial modes via a natural generalization of the beam splitter to a discrete Fourier transform interferometer. Beyond its conceptual significance, this framework offers direct insights into quantum metrology, showing how symmetry properties of input states allow for the computation of explicit precision bounds. By focusing on symmetry, we provide a perspective that simplifies and unifies a range of known results while paving the way for new developments in quantum interference and sensing.
We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong–Ou–Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information.
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.
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).
We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong-Ou-Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information.
Interference experiments like the light and electron double-slit are crucially important to quantum mechanics since they illustrate the core principle of wave-particle duality, by demonstrating the wave-like aspect of particle phenomena. In such experiments, a device is typically required to manipulate the particle-wave dual phenomenon, producing controllable interference. Metasurfaces, with their highly flexible configurability, can serve as more versatile versions of such devices. They are powerful tools capable of modulating a broader category of effects beyond classical interference, such as the quantum Hong-Ou-Mandel (HOM) effect. The HOM effect is caused by interference taking place not between coherent waves from distinct sources which intersect in real space, but rather between parallel processes indistinguishable to the measurement apparatus. Existing research has highlighted the outsized importance of measurement in HOM interferometry, by showing that the occurrence of process interference depends only on indistinguishability at the detectors and nowhere else. We are therefore interested in how quantum measurement occurs in HOM, and how metasurfaces can be used to enhance the HOM effect. In this thesis, we extend a formulation of quantum trajectory theory in two-eigenstate systems to 𝑁-state systems, producing a three-state formalism which serves as a possible description of coincidence pair detection in HOM experiments. We then develop an analytic model of polarisation HOM interferometry capturing both the width and the 𝑔2 ratio of the HOM dip; finally, we design and fabricate a metasurface that exhibits polarisation filtering with respect to two-photon coincidence, whereupon HOM photon bunching occurs only at select metasurface orientations relative to photon polarisation. Our three-state quantum state collapse model offers a promising explanation for how state measurement takes place in an HOM interferometer, where the interferometer output is a superimposition of three two-photon eigenstates. Meanwhile, our interferometer model and experiments provide evidence of successful polarisation filtering in HOM interferometry.