Super-resolved reconstruction of single-photon emitter locations from $g^{(2)}(0)$ maps

TL;DR

The paper addresses the diffraction-limited ambiguity in locating single-photon NV centers by introducing raster-scanned $g^{(2)}(0)$ mapping with an inversion-based reconstruction that infers sub-focal-spot occupancies. It models the forward relation between measured $g^{(2)}(0)$ and pixel occupancies using Gaussian weights and a gradient-based optimization to recover a high-resolution occupancy map. Simulations demonstrate robust reconstruction across spotting radii, scan densities, and emitter counts, including a practical multi-resolution workflow that isolates ROIs for high-resolution scans. The approach provides a practical diagnostic and design tool to guide nanophotonic device integration of NV centers, potentially achieving ~200 nm localization accuracy and reducing experimental effort compared to traditional intensity mapping.

Abstract

Single-photon sources are vital for emerging quantum technologies. In particular, Nitrogen-vacancy (NV) centers in diamond are promising due to their room-temperature stability, long spin coherence, and compatibility with nanophotonic structures. A key challenge, however, is the reliable identification of isolated NV centers, since conventional confocal microscopy is diffraction-limited and cannot resolve emitter distributions within a focal spot. Besides, the associated intensity scanning is a time-expensive procedure. Here, we introduce a raster-scanned $g^{(2)}(0)$ mapping technique combined with an inversion-based reconstruction algorithm. By directly measuring local photon antibunching across the field of view, we extract the effective emitter number within each focal spot and reconstruct occupancy maps on a sub-focal-spot grid. This enables recovery of the number and spatial distribution of emitters within regions smaller than the confocal focal spot, thereby offering possibilities of going beyond the diffraction limit. Our simulations confirm robust reconstruction of NV-center distributions. The method provides a practical diagnostic tool for locating single-photon sources in an efficient and accurate manner, at much lesser time and effort compared to conventional intensity scanning. It offers valuable feedback for nanophotonic device fabrication, supporting more precise and scalable integration of NV-based quantum photonic technologies.

Figures (5)

• Figure 1: Simulated results. (a) $g^{(2)}(\tau)$ for a single NV center in diamond, showing antibunching with $g^{(2)}(0)=0.07$. Inset: $g^{(2)}(0)$ versus the correlation bin width $\Delta t$; the vertical green dashed line marks the $\Delta t$ used in simulations. (b) $g^{(2)}(0)$ as a function of the number of emitters $N$: theory $g^{(2)}(0)=1-\tfrac{1}{N}$ (blue) and simulations (orange).
• Figure 2: (a) shows Spatial distribution of NV centers over a $4\times4~\mu\mathrm{m}^{2}$ sample area, represented on a 20$\times$20-pixel grid. The color scale indicates the number of emitters per pixel and (b) shows raster-scan map of $g^{(2)}(0)$ over the NV-center distribution in a $4\times4~\mu\mathrm{m}^{2}$ field. For each pixel, $g^{(2)}(0)$ is computed from photons collected by an 800 nm diameter focal spot centered on that pixel, as the focal spot is raster-scanned across the NV map. The color scale shows the resulting $g^{(2)}(0)$. Pixels where the focal spot contains no NV centers are left undefined (NaN; white).
• Figure 3: (a) shows reconstructed NV-center distribution obtained by using the $g^{(2)}(0)$ map of Fig. 4. The color scale indicates the number of NV centers per pixel and (b) shows error in reconstructing the original NV center distribution from its $g^{(2)}(0)$ map, plotted versus the maximum number of NV centers per pixel. Error bars indicate the standard deviation across realizations.
• Figure 4: (a) Original NV-center distribution over a $32\times32~\mu\mathrm{m}^{2}$ field sampled at $1.6~\mu\mathrm{m}$ per pixel. (b) $g^{(2)}(0)$ map obtained by raster-scanning (a) with a 6.4 $\mu$m diameter focal spot (low magnification). (c) Emitter distribution reconstructed from (b). (d) Ground-truth emitter distribution within a selected $1.6\times1.6~\mu\mathrm{m}^{2}$ pixel. (e) Local $g^{(2)}(0)$ map of that tile acquired with an 800 nm diameter focal spot (high magnification). (f) Reconstruction from (e).
• Figure 5: Comparison of conventional intensity mapping and reconstruction. (a) Ground-truth NV-center distribution within a $4\times 4~\mu\text{m}^2$ region containing only single emitters. (b) Intensity map obtained by raster-scanning the region with a focal spot. (c) Reconstructed occupancy map from (b), which correctly reproduces single-emitter pixels. (d) Ground-truth distribution for a region containing only multi-emitter sites, but no single emitters. (e) Corresponding intensity map from raster scanning. The weakest intensity locations need to be studied further in the conventional technique. (f) Reconstruction using our algorithm, which correctly identifies the absence of isolated single emitters.