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arXiv:2512.13835 · Communications Physics

Microwave-free vector magnetometry and crystal orientation determination with Nitrogen-Vacancy centers using Bayesian inference

Hilario Espinós, Omkar Dhungel, Arne Wickenbrock, Dmitry Budker, Ricardo Puebla, Erik Torrontegui

quant-phSubmitted Dec 15, 2025• Announced Dec 17, 2025• 1 citation

v1 · Dec 15, 2025 v2 · Jun 16, 2026

Abstract

Nitrogen-vacancy (NV) centers in diamond provide a solid-state platform for quantum sensing. While optically detected magnetic resonance techniques offer high sensitivity, their reliance on microwaves introduces heating and stray electromagnetic fields that can perturb nearby samples. Optical approaches based on cross-relaxation between differently oriented NV centers remove this constraint but have so far required stringent alignment of the external field with crystallographic axes, restricting their practicality. Here we introduce a general framework for microwave-free vector magnetometry at near-zero field that leverages Bayesian inference to extract both the magnetic field vector and the NV orientation directly from photoluminescence maps. An analytical model of cross-relaxation resonances enables efficient inference under arbitrary field and orientation configurations, while naturally incorporating the discrete degeneracies of the NV symmetry. We experimentally demonstrate robust orientation determination and vector-field reconstruction, establishing a general route toward compact and alignment-free NV magnetometers for practical sensing applications.

Comments: 11 pages, 6 figures

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Nitrogen-vacancy (NV) centers in diamond provide a solid-state platform for quantum sensing. While optically detected magnetic resonance techniques offer high sensitivity, their reliance on microwaves introduces heating and stray electromagnetic fields that can perturb nearby samples. Optical approaches based on cross-relaxation between differently oriented NV centers remove this constraint but have so far required stringent alignment of the external field with crystallographic axes, restricting their practicality. Here we introduce a general framework for microwave-free vector magnetometry at near-zero field that leverages Bayesian inference to extract both the magnetic field vector and the NV orientation directly from photoluminescence maps. An analytical model of cross-relaxation resonances enables efficient inference under arbitrary field and orientation configurations, while naturally incorporating the discrete degeneracies of the NV symmetry. We experimentally demonstrate robust orientation determination and vector-field reconstruction, establishing a general route toward compact and alignment-free NV magnetometers for practical sensing applications.

We study cross-relaxation resonances between differently oriented groups of nitrogen-vacancy (NV) centers at small external magnetic fields. These resonances are observed using resonant optical pumping on the NV-center zero phonon line. We suggest a magnetometry protocol that is based on measuring the positions of cross-relaxation resonances on the fluorescence scan. This protocol does not require microwave radiation and can be used to find all components of the unknown magnetic field vector. A room-temperature variant of the protocol with off-resonant optical pumping is also briefly discussed.

Quantum sensors based on nitrogen vacancy (NV) centers in diamond have been a central topic in the sensing community for more than a decade. The extraordinary properties at room temperature of the spin system in diamond have made it one of the most prominent quantum platforms for the development of commercial quantum sensors. In particular, the sensitivity of the electronic spin in NV centers has made diamond-based magnetic sensors of special interest for their potential application in medical, industrial or navigation solutions. However, the use of these sensors for universal vector magnetometry was constrained by the need for previous knowledge on the field being measured to fully exploit their benefits. In this work, we show a method to perform unconditional vector magnetometry without the need of external information on the magnetic field, based only on the spatial arrangement of the diamond and the microwave antenna combination. While previous NV-based vector magnetometry methods require partial knowledge of the magnetic field (e.g. a calibrated bias field), we exploit the possibilities of selecting particular directions of the spins in the diamond with elliptically polarized microwave fields. We prove that our method allows to estimate both magnitude and direction of external magnetic fields without further assumptions or constraints.

The nitrogen-vacancy (NV) color center in diamond has found applications in magnetometry across various geometrical scales. In particular, vector magnetometry using hand-held devices with low power consumption is of interest for mobile and geological applications. However, such a device requires efficient driving of the four different orientations of the NV center, thus placing demands on a broadband microwave resonator that provides a uniform and highly insensitive microwave magnetic field at the resonance frequencies of the NV centers. Here, we propose a unique planar resonator design that enables efficient driving of all four orientations of NV color centers over a 100 MHz range with only 0.5 W of microwave input power and 250 mW of laser power, allowing vector magnetic field measurements. Using the planar resonator to drive NV centers in diamond, a compact vector magnetometer was fabricated and experimentally studied. The sensitivity of the device is about

{1.2\text{ nT}}/{\sqrt{\text{Hz}}}\;

. While this is not a record sensitivity for diamond-based magnetometers, this device occupies its own niche as a compact hand-held magnetometer.

We study cross-relaxation-based magnetometry in ensembles of nitrogen-vacancy (NV) centers using the protocol suggested by Akhmedzhanov et al. [R. Akhmedzhanov, L. Gushchin, N. Nizov, V. Nizov, D. Sobgayda, I. Zelensky, and P. Hemmer, Microwave-free magnetometry based on cross-relaxation resonances in diamond nitrogen-vacancy centers, Phys. Rev. A 96, 013806 (2017)]. We suggest a processing scheme that allows us to perform measurements without precise sample orientation. It is shown theoretically and experimentally that using an additional magnetic field can significantly simplify vector magnetic-field measurements.

We present a novel method for full vector magnetometry using nitrogen-vacancy (NV) centers. In contrast to conventional optically detected magnetic resonance techniques, our method employs two distinct broadband microwave pulses and measures them after transmission through the NV sensor medium, thus capturing the line splitting of the ground state triplet due to the Zeeman effect. Two orthogonally polarized microwave pulses allow resolving all magnetic field components independently by reading out differently oriented NV centers. Simulated data is analyzed using deep neural networks, whose efficacy we expect to translate very well to experiments. Our method yields sensitivities between

5~\mathrm{pT}/\sqrt{\mathrm{Hz}}

and

100~\mathrm{pT}/\sqrt{\mathrm{Hz}}

across different magnetic field vector components, while achieving approximately

\mathrm{nT}

accuracy at a signal-to-noise (SNR) ratio of

70~\mathrm{dB}

. By being capable of accurately measuring magnetic fields down to

25~\mathrm{μT}

, the need for a bias field beyond Earth's magnetic field is eliminated.

We demonstrate a robust, scale-factor-free vector magnetometer, which uses a closed-loop frequency-locking scheme to simultaneously track Zeeman-split resonance pairs of nitrogen-vacancy (NV) centers in diamond. This technique offers a three-orders-of-magnitude increase in dynamic range compared to open-loop methodologies; is robust against fluctuations in temperature, resonance linewidth, and contrast; and allows for simultaneous interrogation of multiple transition frequencies. By directly detecting the resonance frequencies of NV centers oriented along each of the diamond's four tetrahedral crystallographic axes, we perform full vector reconstruction of an applied magnetic field.