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arXiv:2508.13438 · Optica Quantum

Towards quantum-limited spatial resolution of NV-diamond magnetometry

Nico Deshler, Nicolas Deshler, Ayan Majumder, Kasturi Saha, Saikat Guha

Published Jun 15, 2026• 0 citations
arXivHTMLPDF

Abstract

Optically addressable ensembles of solid-state defects, such as nitrogen-vacancy (NV) centers, are a leading modality for imaging-based magnetometry, thermometry, and strain sensing. However, monitoring the fluorescence of individual defects within a sub-diffraction ensemble remains an outstanding challenge that currently limits access to atomic-scale features and dynamics. For compact clusters of NVs, we formulate imaging-based atomic sensing as a low-dimensional multiparameter estimation task in which one seeks to localize each defect and quantify the field strength in its immediate vicinity. In this work, we employ optical spatial mode demultiplexing (SPADE) to enhance localization and brightness estimation accuracy at sub-diffraction scales. Specifically, we develop a two-stage sensing protocol that augments direct imaging by projecting the incoming optical field onto point spread function (PSF)-adapted, i.e., PAD spatial modes and Yuen–Kennedy–Lax (YKL) spatial modes, enabling efficient extraction of emitter positions and brightnesses. The YKL-SPADE measurement used for brightness estimation is shown to be quantum-optimal in the case of two emitters and establishes a new connection between quantum detection and estimation theories. We numerically evaluate the statistical performance of our protocol for sub-diffraction optically detected magnetic resonance (ODMR) and Rabi sensing experiments. Compared to conventional focal plane intensity measurements, our protocol improves emitter localization accuracy by 6× and brightness estimation accuracy by 2× for tightly confined ensembles, residing well below the diffraction limit.

DOI
10.1364/opticaq.580302

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Optically addressable ensembles of solid-state defects, such as nitrogen-vacancy (NV) centers, are a leading modality for imaging-based magnetometry, thermometry, and strain sensing. However, monitoring the fluorescence of individual defects within a sub-diffraction ensemble remains an outstanding challenge that currently limits access to atomic-scale features and dynamics. For compact clusters of NVs, we formulate imaging-based atomic sensing as a low-dimensional multiparameter estimation task in which one seeks to localize each defect and quantify the field strength in its immediate vicinity. In this work, we employ optical spatial mode demultiplexing (SPADE) to enhance localization and brightness estimation accuracy at sub-diffraction scales. Specifically, we develop a two-stage sensing protocol that augments direct imaging by projecting the incoming optical field onto point spread function (PSF)-adapted, i.e., PAD spatial modes and Yuen–Kennedy–Lax (YKL) spatial modes, enabling efficient extraction of emitter positions and brightnesses. The YKL-SPADE measurement used for brightness estimation is shown to be quantum-optimal in the case of two emitters and establishes a new connection between quantum detection and estimation theories. We numerically evaluate the statistical performance of our protocol for sub-diffraction optically detected magnetic resonance (ODMR) and Rabi sensing experiments. Compared to conventional focal plane intensity measurements, our protocol improves emitter localization accuracy by 6× and brightness estimation accuracy by 2× for tightly confined ensembles, residing well below the diffraction limit.
In modern-day quantum metrology, quantum sensors are widely employed to detect weak magnetic fields or nanoscale signals. Quantum devices, exploiting quantum coherence, are inevitably connected to physical constants and can achieve accuracy, repeatability, and precision approaching fundamental limits. As a result, these sensors have shown utility in a wide range of research domains spanning both science and technology. A rapidly emerging quantum sensing platform employs atomic-scale defects in crystals. In particular, magnetometry using nitrogen-vacancy (NV) color centers in diamond has garnered increasing interest. NV systems possess a combination of remarkable properties, optical addressability, long coherence times, and biocompatibility. Sensors based on NV centers excel in spatial resolution and magnetic sensitivity. These diamond-based sensors promise comparable combination of high spatial resolution and magnetic sensitivity without cryogenic operation. The above properties of NV magnetometers promise increasingly integrated quantum measurement technology, as a result, they have been extensively developed with various protocols and find use in numerous applications spanning materials characterization, nuclear magnetic resonance (NMR), condensed matter physics, paleomagnetism, neuroscience and living systems biology, and industrial vector magnetometry. In this chapter, NV centers are explored for magnetic sensing in a number of contexts. In general, we introduce novel regimes for magnetic-field probes with NV ensembles. Specifically, NV centers are developed for sensitive magnetometers for applications where microwaves (MWs) are prohibitively invasive and operations need to be carried out under zero ambient magnetic field. The primary goal of our discussion is to improve the utility of these NV center-based magnetometers.
The NV defect center in diamond forms a pseudo-atomic quantum system with discreet optically excitable transitions between ground and excited states in the gap between valence and conduction bands, making the NV center a deep-level defect center in diamond. For the negatively charged NV center (NV-), both the ground and excited states are spin triplets (S=1) and coupling between optical and spin states provides unique opportunities for optical detection of magnetic resonance (ODMR) and quantum metrology under ambient conditions. As an atomically sized point defect that is stable in single nanodiamonds as small as a few nanometers, the NV center enables spin based imaging of temperature, electric fields, magnetic fields and mechanical strain with nanoscale spatial resolution. Made of carbon, nanodiamonds are also ideal nanoparticles for use in biological systems, exhibiting extremely low cytotoxicity, no photo bleaching and exceptional contrast in transmission electron and light microscopy. With the ability to act as both a passive, non perturbing sensor (e.g. a diamagnetic material used for sensing magnetic fields) and a connection point for two way, direct coupling of far field optics to NV−^-− spins and indirectly to the highly localized neighborhood of atoms, electronic states and phonon modes in the local vicinity, NV diamond provides a route to nanoscale field sensing and spin based optical microscopy. These sensors are also stable in nanodiamonds. For nanoparticles, the reduction in particle diameter dramatically enhances the proportion of the material that is surface exposed, enhancing any surface related properties. Nitrogen Vacancy centers in nanodiamonds provide another example of material properties that vary with particle size. In chapter 5, evidence that modulation of nanodiamonds fluorescent emissions by electrical perturbations in their surrouding environment allows transduction of local electrodynamics into a far field optical signal capable of mapping action potentials in cardiomyocytes in presented. The unifying theme for all of the work presented in this dissertation is to enable the use of magnetic resonance signals and interactions for imaging and sensing in previously inaccessible regimes. The specific focus is on methods and techniques to enable nanoscale physical sensing and functional imaging in live tissues, with the ultimate aim to lay the predicate for the combination of both without compromise.
Nitrogen vacancy (NV) centers in diamond are atom-scale defects that can be used to sense magnetic fields with high sensitivity and spatial resolution. Typically, the magnetic field is measured by averaging sequential measurements of single NV centers, or by spatial averaging over ensembles of many NV centers, which provides mean values that contain no nonlocal information about the relationship between two points separated in space or time. Here, we propose and implement a sensing modality whereby two or more NV centers are measured simultaneously, and we extract temporal and spatial correlations in their signals that would otherwise be inaccessible. We demonstrate measurements of correlated applied noise using spin-to-charge readout of two NV centers and implement a spectral reconstruction protocol for disentangling local and nonlocal noise sources.
Shallow nitrogen-vacancy (NV) centers are promising candidates for high-precision sensing applications; these defects, when positioned a few nanometers below the surface, provide an atomic-scale resolution along with substantial sensitivity. However, the dangling bonds and impurities on the diamond surface result in a complex environment which reduces the sensitivity and is unique to each shallow NV center. To avoid the environment's detrimental effect, we apply feedback-based quantum optimal control. We first show how a direct search can improve the initialization and readout process. In a second step, we optimize microwave pulses for pulsed optically detected magnetic resonance (ODMR) and Ramsey measurements. Throughout the sensitivity optimizations, we focus on robustness against errors in the control field amplitude. This feature not only protects the protocols' sensitivity from drifts but also enlarges the sensing volume. The resulting ODMR measurements produce sensitivities below $1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{T}$ ${\mathrm{Hz}}^{\ensuremath{-}\frac{1}{2}}$ for an 83% decrease in control power, increasing the robustness by approximately one third. The optimized Ramsey measurements produce sensitivities below 100 nT ${\mathrm{Hz}}^{\ensuremath{-}\frac{1}{2}}$ giving a twofold sensitivity improvement. Being on par with typical sensitivities obtained via single NV magnetometry, the complementing robustness of the presented optimization strategy may provide an advantage for other NV-based applications.
The sharp optical resonances of NV- centers in diamond at cryogenic temperatures offer powerful new capabilities for material characterization, but extracting the most detailed information typically requires careful calibration of individual sensors, limiting scalability. In this work, we use resonant photoluminescence excitation imaging to optically resolve and monitor hundreds of individual NVs across large fields of view, enabling statistical analysis of their spatial distribution with sub-diffraction resolution. This multiplexed, non-destructive approach allows quantum sensors to characterize the material platform they inhabit. Focusing on CVD-grown diamond, we uncover significant deviations from random distributions, including an unexpectedly high occurrence of closely spaced clusters comprising two or more NVs. These findings suggest non-Poissonian formation dynamics and point to spatially correlated defect generation mechanisms. Beyond offering insight into diamond growth and NV center formation, our approach enables the scalable identification of naturally occurring NV clusters - configurations that are promising for entanglement-assisted quantum information protocols and correlated sensing - and establishes a path toward structural and electronic defect analysis in various material hosts at the single-emitter level.
We experimentally demonstrate precision addressing of single-quantum emitters by combined optical microscopy and spin resonance techniques. To this end, we use nitrogen vacancy (NV) color centers in diamond confined within a few ten nanometers as individually resolvable quantum systems. By developing a stochastic optical reconstruction microscopy (STORM) technique for NV centers, we are able to simultaneously perform sub-diffraction-limit imaging and optically detected spin resonance (ODMR) measurements on NV spins. This allows the assignment of spin resonance spectra to individual NV center locations with nanometer-scale resolution and thus further improves spatial discrimination. For example, we resolved formerly indistinguishable emitters by their spectra. Furthermore, ODMR spectra contain metrology information allowing for sub-diffraction-limit sensing of, for instance, magnetic or electric fields with inherently parallel data acquisition. As an example, we have detected nuclear spins with nanometer-scale precision. Finally, we give prospects of how this technique can evolve into a fully parallel quantum sensor for nanometer resolution imaging of delocalized quantum correlations.