Machine-learning-enhanced quantum sensors for accurate magnetic field imaging

Diamond nanoparticles (nanodiamonds) offer an attractive opportunity to achieve high spatial resolution because they can easily be close to the target within a few 10 nm simply by attaching them to its surface [8]. A physical model for such a randomly oriented nanodiamond ensemble (NDE) is available [8], but the complexity of actual experimental conditions still limits the accuracy of deducing magnetic fields. Here, we demonstrate magnetic field imaging with high accuracy of 1.8 µT combining NDE and machine learning without any physical models. We also discover the field direction dependence of the NDE signal, suggesting the potential application for vector magnetometry and improvement of the existing model. Our method further enriches the performance of NDE to achieve the accuracy to visualize mesoscopic current and magnetism in atomic-layer materials [9-13] and to expand the applicability in arbitrarily shaped materials [7], including living organisms [14, 15]. This achievement will bridge machine learning and quantum sensing for accurate measurements. The nitrogen-vacancy (NV) center in diamond [Figure 1(a)] is a point defect where a nitrogen atom replaces a carbon atom in the lattice accompanied by a neighboring vacancy. By measuring its photoluminescence intensity while irradiating the laser and microwaves, NV's electron spin resonance can be detected, which is called optically detected microwave resonance (ODMR) [16]. As the NV's spin level splits against the magnetic field in the direction of the NV symmetry axis (111) due to the Zeeman effect [17], the determination of the ODMR frequency serves as quantum sensing of the field [3]. To obtain a nanoscale spatial resolution, we must attach the NV centers close to the sample within a few 10 nm [18].