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arXiv:2309.06883 · Physical Review Letters

Estimation with Ultimate Quantum Precision of the Transverse Displacement between Two Photons via Two-Photon Interference Sampling Measurements

Danilo Triggiani, Vincenzo Tamma

Published Apr 30, 2024• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.132.180802

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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.
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.
Abstract We present a quantum sensing protocol for the simultaneous estimation of the difference in the localization parameters of two single-photon sources, paving the way to single-photon 3D imaging and 3D nanoscopy beyond the diffraction limit. This is achieved by exploiting two-photon interference of the two emitted photons at a beam splitter via sampling measurements in the frequency and transverse momenta at the output. We prove theoretically that this technique reaches the ultimate sensitivity in the 3D relative localization of two emitters, already with a number of sampling measurements of ∼2000\sim 2000∼2000 ∼ 2000 and a bias in the three localization parameters below 1%1\%1% 1 % . These results are independent of the values of the localization parameters to estimate.
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 protocol for three-dimensional estimation of the difference between the momenta of two photons based on spatially resolved interferometric sampling measurements. The protocol attains ultimate quantum precision in the simultaneous estimation of the components of the relative momentum for any values of the parameters already with ∼2000\sim 2000∼2000 sampling measurements and a bias below 1%1\%1%. These results identify 3D spatially resolved two-photon interference as an efficient tool for multi-parameter quantum sensing, with potential applications in high-precision 3D localization, refractometry, and near-field calibration in free-space quantum technologies.
We demonstrate the ultimate sensitivity allowed by quantum physics in the estimation of the time delay between two photons by measuring their interference at a beam splitter through frequency-resolving sampling measurements. This sensitivity can be increased quadratically by decreasing the photonic temporal bandwidth even at values smaller than the time delay when standard two-photon interferometers become inoperable and without adapting the path of the reference photon, nor the need of time-resolving detectors with an unfeasible high resolution. Applications can range from the more feasible imaging of nanostructures, including biological samples, and nanomaterial surfaces to quantum enhanced estimation based on frequency-resolved boson sampling in optical networks.