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Physical Review Applied

Polarization-Assisted Vector Magnetometry with No Bias Field Using an Ensemble of Nitrogen-Vacancy Centers in Diamond

Franz Münzhuber, Florian Bayer, Vera Marković, J. Brehm, Johannes Kleinlein, Laurens W. Molenkamp, T. Kießling

Published Jul 20, 2020• 17 citations
Publisher

Abstract

Nitrogen-vacancy ($\mathrm{N}$-$V$) centers in diamond are among the best-studied quantum-based sensors for a wide range of applications. Here, we demonstrate an optical polarization-based method for full vector magnetometry using ensembles of $\mathrm{N}$-$V$ centers. The anisotropy of the electric dipole moments of the $\mathrm{N}$-$V$ centers enables the assignment of the different magnetic field split transitions in the optically detected magnetic resonance spectra by appropriately setting the optical polarization in the excitation and/or detection of the $\mathrm{N}$-$V$ photoluminescence signal. By further employing the optical-selection rules for the driving microwave field, we show how the full vector of the investigated magnetic field can be restored without the need to apply external bias fields. We discuss different $\mathrm{N}$-$V$-center orientation implementations and limitations toward common approximations used in the $\mathrm{N}$-$V$ magnetometry literature for our approach.

DOI
10.1103/physrevapplied.14.014055

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Nitrogen-vacancy (N\mathrm{N}N-VVV) centers in diamond are among the best-studied quantum-based sensors for a wide range of applications. Here, we demonstrate an optical polarization-based method for full vector magnetometry using ensembles of N\mathrm{N}N-VVV centers. The anisotropy of the electric dipole moments of the N\mathrm{N}N-VVV centers enables the assignment of the different magnetic field split transitions in the optically detected magnetic resonance spectra by appropriately setting the optical polarization in the excitation and/or detection of the N\mathrm{N}N-VVV photoluminescence signal. By further employing the optical-selection rules for the driving microwave field, we show how the full vector of the investigated magnetic field can be restored without the need to apply external bias fields. We discuss different N\mathrm{N}N-VVV-center orientation implementations and limitations toward common approximations used in the N\mathrm{N}N-VVV magnetometry literature for our approach.
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 pT/Hz5~\mathrm{pT}/\sqrt{\mathrm{Hz}}5 pT/Hz​ and 100 pT/Hz100~\mathrm{pT}/\sqrt{\mathrm{Hz}}100 pT/Hz​ across different magnetic field vector components, while achieving approximately nT\mathrm{nT}nT accuracy at a signal-to-noise (SNR) ratio of 70 dB70~\mathrm{dB}70 dB. By being capable of accurately measuring magnetic fields down to 25 μT25~\mathrm{μT}25 μT, the need for a bias field beyond Earth's magnetic field is eliminated.
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.
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.
Accurate measurement of vector magnetic fields is critical for applications including navigation, geoscience, and space exploration. Nitrogen-vacancy ( N V ) center spin ensembles offer a promising solution for high-sensitivity vector magnetometry, as their different orientations in the diamond lattice measure different components of the magnetic field. However, the bias magnetic field typically used to separate signals from each N V orientation introduces inaccuracy from drifts in permanent magnets or coils. Here, we present a novel bias-field-free approach that labels the N V orientations via the direction of the microwave (MW) field in a variable-pulse-duration Ramsey sequence used to manipulate the spin ensemble. Numerical simulations demonstrate the possibility to isolate each orientation’s signal with subnanotesla accuracy in most terrestrial fields, even without precise MW field calibration, at only a moderate cost to sensitivity. We also provide proof-of-principle experimental validation, observing relevant features that evolve as expected with the applied magnetic field. Looking forward, by removing a key source of drift, the proposed protocol lays the groundwork for future deployment of N V magnetometers in high-accuracy or long-duration missions.
Nitrogen-vacancy (NV) centers in diamond are a leading platform for vector magnetometry, offering intrinsic sensitivity to both the magnitude and direction of magnetic fields. NV magnetometers typically rely on an external bias field to lift the degeneracy of the ground-state spin sublevels, enabling spectral discrimination of different NV orientations and spin transitions. At high accuracy, however, such a bias field systematically introduces errors through thermal, mechanical, and hysteretic drifts, thus hindering the accurate measurement of the magnetic field of interest. Several strategies have been proposed to address this limitation, including optical polarization-based orientation labeling, optical anisotropy, strong coupling to nearby nuclear spins, circular microwave polarization, and tailored pulse sequences. In this work, we introduce an optimization-based pulse-shaping control framework that enables selective and robust manipulation of NV ensembles without relying on a static bias field. Our method achieves both orientation-selective and subspace-selective control through optimal temporal modulation of the driving fields, providing a route to resolving spectral overlaps in degenerate NV systems.
On-chip magnetic field sensing with nitrogen-vacancy (NV) centers in diamond requires scalable integration of 3D waveguides into diamond substrates. Here, we develop a sensing array device with an ensemble of shallow implanted NV centers integrated with arrays of laser-written waveguides for excitation and readout of NV signals. Our approach enables an easy-to-operate on-chip magnetometer with a pixel size proportional to the Gaussian mode area of each waveguide. The performed continuous wave optically detected magnetic resonance on each waveguide gives an average dc-sensitivity value of (195±3) nT/Hz, which can be improved with lock-in-detection or pulsed-microwave sequences. We apply a magnetic field to separate the four NV crystallographic orientations of the magnetic resonance and then utilize a DC current through a straight wire antenna close to the waveguide to prove the sensor capabilities of our device. We reconstruct the complete vector magnetic field in the NV crystal frame using three different NV crystallographic orientations. By knowing the polarization axis of the waveguide mode, we project the magnetic field vector into the lab frame.