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arXiv:2602.19772 · Quantum Science and Technology

Multiphoton Hong-Ou-Mandel Interference Enables Superresolution of Bright Thermal Sources

Aiman Khan, Danilo Triggiani, Vincenzo Tamma

quant-phSubmitted Feb 23, 2026• Announced Feb 24, 2026• 0 citations
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Abstract

We present a quantum optical scheme for imaging transversely displaced thermal sources of arbitrary intensities by employing multiphoton interference with a reference single-photon Fock state at a beamsplitter. Obtaining an analytical form for transverse momenta-resolved $L$-photon probabilities in either output, we show via Fisher information analysis that separation estimators built using interference sampling of multiphoton events exhibit significantly enhanced precision vis-à-vis existing imaging schemes over a wide range of separations and brightness. Even-photon-number coincidences exhibit constant precision in the sub-Rayleigh regime, demonstrating quantum superresolution of our scheme beyond the diffraction limit. For sources emitting on average $N_s\sim1$ photon per frame (such as in IR emission of thermal sources), precision bounds for our scheme scale linearly in $N_s$, exemplifying an enhanced precision of estimators in relation to weak sources $N_s\ll1$, and matching the ultimate quantum scaling. Finally, transverse momenta resolution in the Fourier plane produces finite imaging precisions for intermediate and large source separations using coarse pixel sizes of order $δy\sim100\,μ\mathrm{m}$ for exemplary image spot sizes $σ_x \sim 0.1\, μ\mathrm{m}$, in contrast with existing schemes of diffraction-limited direct imaging and superresolved inversion interferometric imaging that are severely degraded by coarse pixel sizes and have limited use. Combining the relatively straightforward sensing operation of Hong-Ou-Mandel interferometers with multiphoton coincidence detection of arbitrarily bright thermal sources and inner variable resolution of transverse photonic momenta, our scheme offers a robust alternative to non-invasive single-particle tracking and imaging of bright sources in nanoscopic chemical and biological systems.

Journal reference
Aiman Khan et al 2026 Quantum Sci. Technol. 11 045033
DOI
10.1088/2058-9565/ae9abd
Comments
20 pages, 8 figures; comments are welcome

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We present a quantum optical scheme for imaging transversely displaced thermal sources of arbitrary intensities by employing multiphoton interference with a reference single-photon Fock state at a beamsplitter. Obtaining an analytical form for transverse momenta-resolved LLL-photon probabilities in either output, we show via Fisher information analysis that separation estimators built using interference sampling of multiphoton events exhibit significantly enhanced precision vis-à-vis existing imaging schemes over a wide range of separations and brightness. Even-photon-number coincidences exhibit constant precision in the sub-Rayleigh regime, demonstrating quantum superresolution of our scheme beyond the diffraction limit. For sources emitting on average Ns∼1N_s\sim1Ns​∼1 photon per frame (such as in IR emission of thermal sources), precision bounds for our scheme scale linearly in NsN_sNs​, exemplifying an enhanced precision of estimators in relation to weak sources Ns≪1N_s\ll1Ns​≪1, and matching the ultimate quantum scaling. Finally, transverse momenta resolution in the Fourier plane produces finite imaging precisions for intermediate and large source separations using coarse pixel sizes of order δy∼100 μmδy\sim100\,μ\mathrm{m}δy∼100μm for exemplary image spot sizes σx∼0.1 μmσ_x \sim 0.1\, μ\mathrm{m}σx​∼0.1μm, in contrast with existing schemes of diffraction-limited direct imaging and superresolved inversion interferometric imaging that are severely degraded by coarse pixel sizes and have limited use. Combining the relatively straightforward sensing operation of Hong-Ou-Mandel interferometers with multiphoton coincidence detection of arbitrarily bright thermal sources and inner variable resolution of transverse photonic momenta, our scheme offers a robust alternative to non-invasive single-particle tracking and imaging of bright sources in nanoscopic chemical and biological systems.
We present a quantum sensing scheme achieving the ultimate quantum sensitivity in the estimation of the transverse displacement between two photons interfering at a balanced beam splitter, based on transverse-momentum sampling measurements at the output. This scheme can possibly lead to enhanced high-precision nanoscopic techniques, such as superresolved single-molecule localization microscopy with quantum dots, by circumventing the requirements in standard direct imaging of camera resolution at the diffraction limit, and of highly magnifying objectives. Interestingly, we show that our interferometric technique achieves the ultimate spatial precision in nature irrespectively of the overlap of the two displaced photonic wave packets, while its precision is only reduced of a constant factor for photons differing in any nonspatial degrees of freedom. This opens a new research paradigm based on the interface between spatially resolved quantum interference and quantum-enhanced spatial sensitivity.
The Rayleigh's criterion imposes a minimum separation between two incoherent sources for them to be distinguishable via classical methods. In this work, we demonstrate the emergence of two-photon beats from the interference of a single reference photon and a photon coming from one of two transversally displaced incoherent sources. We also show that, apart from a factor of 2, the ultimate quantum precision in the estimation of any value of the distance between two weak thermal sources is achievable independently of the spatial structure of wave packet by performing a relatively low number of sampling measurements of the transverse momenta of the interfering photons without the need for any additional optics. The feasibility of this technique makes it an optimal candidate for important applications in microscopy, astronomy, and remote sensing.
We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cramér-Rao bound that, contrary to the Rayleigh limit in conventional direct imaging, quantum mechanics does not mandate any loss of precision in estimating even deep sub-Rayleigh separations. We propose two coherent measurement techniques, easily implementable using current linear-optics technology, that approach the quantum limit over an arbitrarily large range of separations. Our bound is valid for arbitrary source strengths, all regions of the electromagnetic spectrum, and for any imaging system with an inversion-symmetric point-spread function. The measurement schemes can be applied to microscopy, optical sensing, and astrometry at all wavelengths.
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.
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First, we show that the problem of estimating the separation between two pointlike sources is equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Using this representation, we establish the ultimate precision bound for resolving two pointlike sources in an arbitrary quantum state, with a simple formula for the specific case of two thermal sources. We find that the precision bound scales with the number of collected photons according to the standard quantum limit. Then, we determine the sources whose separation can be estimated optimally, finding that quantum-correlated sources (entangled or discordant) can be superresolved at the sub-Rayleigh scale. Our results apply to a variety of imaging setups, from astronomical observation to microscopy, exploiting quantum detection as well as source engineering.
It has been shown through quantum estimation theory that Rayleigh’s limit can be avoided for single-lens imaging, referred to as superresolution. The quantum estimation approach has recently been used to show superresolution is also possible for imaging based on interferometer arrays in the weak source limit. Following this line of discussion, we consider the resolution limit of estimating the separation between two point sources of arbitrary strength using interferometer arrays. By carefully designing the measurement, we find it is possible to overcome the well-known resolution limit of interferometer arrays as determined by the longest baseline. We construct an optimal measurement to achieve superresolution using linear beam-splitters and photon-number resolved detection.