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arXiv:2510.11720 · Physical Review A

Magnetometry with broadband microwave fields in nitrogen-vacancy centers in diamond

Arezoo Afshar, Andrew H. Proppe, Noah Lupu-Gladstein, Lilian Childress, Aaron Z. Goldberg, Khabat Heshami

Published May 15, 2026• 1 citation
arXivHTMLPDF

Abstract

Nitrogen-vacancy (NV) centers in diamond are optically addressable and versatile light-matter interfaces with practical application in magnetic field sensing, offering the ability to operate at room temperature and reach sensitivities below pT/$\sqrt{\mathrm{Hz}}$. We propose an approach to simultaneously probe all of the magnetically sensitive states using a broadband microwave field and demonstrate that it can be used to measure the external DC magnetic field strength with sensitivities on the order of 10~pT/$\sqrt{\mathrm{Hz}}$. We develop tools for analyzing the temporal signatures in the transmitted broadband microwaves to estimate the magnetic field, comparing maximum likelihood estimation based on minimizing the Kullback-Leibler divergence to various neural network models, and both methods independently reach practical sensitivities. These results are achieved without optimizing parameters such as the bandwidth, and shape of the probing microwave field such that further improvements in sensitivity can be envisioned. Our results motivate novel implementations of NV-based magnetic sensors with the potential for vectorial magnetic field detection at 1-10 kHz update rates and improved sensitivities without requiring a bias magnetic field.

DOI
10.1103/dzyt-xj8m

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Nitrogen-vacancy (NV) centers in diamond are optically addressable and versatile light-matter interfaces with practical application in magnetic field sensing, offering the ability to operate at room temperature and reach sensitivities below pT/Hz\sqrt{\mathrm{Hz}}Hz​. We propose an approach to simultaneously probe all of the magnetically sensitive states using a broadband microwave field and demonstrate that it can be used to measure the external DC magnetic field strength with sensitivities on the order of 10~pT/Hz\sqrt{\mathrm{Hz}}Hz​. We develop tools for analyzing the temporal signatures in the transmitted broadband microwaves to estimate the magnetic field, comparing maximum likelihood estimation based on minimizing the Kullback-Leibler divergence to various neural network models, and both methods independently reach practical sensitivities. These results are achieved without optimizing parameters such as the bandwidth, and shape of the probing microwave field such that further improvements in sensitivity can be envisioned. Our results motivate novel implementations of NV-based magnetic sensors with the potential for vectorial magnetic field detection at 1-10 kHz update rates and improved sensitivities without requiring a bias magnetic field.
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.
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.
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) center in diamond has attracted considerable attention as a highly sensitive quantum sensor that can operate at room temperature. In particular, continuous-wave optically detected magnetic resonance (CW-ODMR) is promising for a wide range of applications because of its simplicity. However, conventional AC magnetic-field sensing schemes based on CW-ODMR suffer from a limited detection bandwidth: the detectable frequency is either fixed by intrinsic physical parameters of the NV center or, even when tunable, restricted to a narrow range of only a few MHz. Here, we propose a broadband AC magnetometry scheme based on CW-ODMR with NV centers using microwave-driven dressed states.Through theoretical analysis and numerical simulations, we show that the proposed scheme enables the detection of AC magnetic fields with frequencies up to the order of 100 MHz, which has been difficult to achieve using conventional CW-ODMR-based methods.
Microwave magnetometry is essential to a variety of modern electronic techniques, most notably integrated circuits. The nitrogen-vacancy center in diamond has shown the ability of nanoscale resolution for the microwave magnetic field measurement and imaging. However, the characterization of the wideband magnetic field remains a challenge. Here we experimentally demonstrated a wideband microwave magnetometry with an off-resonance protocol based on the Bloch-Siegert shift effect. The off-resonance microwave magnetic field shifts the energy level of the nitrogen-vacancy center. It results in a phase accumulation during the evolution of the superposition state of the quantum sensor. According to this effect, by optimizing the evolution time, we experimentally verified the bandwidth widening of an order of magnitude compared with the Rabi oscillation, i.e., on-resonance method with an acceptable decrease of the sensitivity. In addition, we extracted the microwave frequency with a two-qubit system, which consists of a nitrogen-vacancy center and a nearby 13C^{13}\mathrm{C}13C nucleus. This approach enables the building of a wideband and potentially nanoscale microwave magnetometry to allow various potential applications, such as electronic circuits development.
The measurement of vector magnetic fields with high sensitivity and spatial resolution is important for both fundamental science and engineering applications. In particular, magnetic-field sensing with nitrogen-vacancy (NV) centers in diamond is a promising approach that can outperform existing methods. Recent studies have demonstrated vector dc magnetic-field sensing with perfectly aligned NV centers, which showed a higher readout contrast than NV centers having four equally distributed orientations. However, to estimate the azimuthal angle of the target magnetic field with respect to the NV axis in these previous approaches, it is necessary to apply a strong reference dc magnetic field, which can perturb the system to be measured. This is a crucial problem, especially when attempting to measure vector magnetic fields from materials that are sensitive to applied dc magnetic fields. Here, we propose a method to measure vector dc magnetic fields using perfectly aligned NV centers without reference dc magnetic fields. This method can be performed even with a single NV center. More specifically, we use the direction of linearly polarized microwave fields to induce Rabi oscillation as a reference and we estimate the azimuthal angle of the target fields from the Rabi frequency. We further demonstrate the potential of our method to improve sensitivity by using entangled states to overcome the standard quantum limit. Our method of using a reference microwave field is an alternative technique for sensitive vector dc magnetic-field sensing.