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

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-\`a-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 $\delta y\sim100\,\mu \mathrm{m}$ for exemplary image spot sizes $\sigma_x \sim 0.1\, \mu \mathrm{m}$, 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.