Kensuke Kobayashi (Professor, Institute for Physics of Intelligence/Department of Physics)

Yuto Ashida (Associate Professor, Department of Physics, Institute for Physics of Intelligence)

Kento Sasaki (Assistant Professor, Department of Physics)

Mota Tsukamoto (Graduate student, Department of Physics)

Key points of the presentation

• Machine learning of quantum sensor properties in nanodiamonds enables accurate imaging of magnetic fields.
• Expected to be applied to local magnetic field measurement applicable to measurement targets with various surface geometries, such as magnetic materials, electronic devices, organisms, and minerals.

Summary of Presentation

A group of graduate students led by Professor Kensuke Kobayashi, Assistant Professor Kento Sasaki, and Mouta Tsukamoto at the Graduate School of Science, The University of Tokyo, together with Associate Professor Yuto Ashida of the same Graduate School, have succeeded in machine learning the precise measurement results of the magnetic field dependence of the nitrogen vacancy centers ^{(Note 1)} in nanodiamonds ^{(Note 2)} and in imaging magnetic fields more accurately than the conventional method. The result is more accurate magnetic field imaging than the conventional method.

The quantum state of the electron spin ^{(Note 3} ) of the nitrogen vacancy center in diamond is applied to quantum measurement ^{(Note 4)} because of its rare property that it remains for a long time even at room temperature and can be optically read out. In this study, we succeeded in precise magnetic field imaging by machine learning the magnetic field dependence of a population of membrane-distributed nanodiamonds. We measured diamond spectra while precisely controlling the magnetic field using a Helmholtz coil ^{(Note 5)} and successfully generated a function that accurately estimates the magnetic field strength by using Gaussian process regression, known as model-free machine learning. This research is a powerful tool in the investigation of magnetic field distribution on surfaces of various geometries, including magnetic materials, electronic devices, organisms, and minerals.

Publication Details

Research Background
Magnetic field measurements are used in a wide range of research fields, including physics, biology, and geology. In particular, measurement methods with high spatial resolution are useful for the evaluation of materials with microscopic structures, such as magnetic materials and electronic devices. In general, the smaller the size of the magnetic field sensor and the closer it can be brought to the object being measured, the higher the spatial resolution.

Since 2008, when a highly sensitive and high spatial resolution magnetic field measurement method using nitrogen vacancy centers in diamond, which are atom-sized, was proposed, this method has been studied worldwide. Techniques have been developed to adhere diamond to the object to be measured, such as incorporating it into an interatomic microscope ^{(Note 6)} or attaching it to the surface of the object to be measured by making it thinner and more flexible. These techniques require advanced microfabrication technology to process diamond. Recently, a simple technique for imaging magnetic fields and temperatures has emerged, which simply involves spraying a population of nanodiamonds containing nitrogen-vacancy centers as a film. The advantages of this technique are the ease of procurement of nanodiamonds and its direct application to objects with arbitrary surface topography. However, the disparate crystallographic orientation of the nanodiamonds during scattering makes it difficult to accurately estimate the magnetic field from their sensor signals.

Research Details
The research group generated a nanodiamond film on a cover glass and precisely investigated its magnetic field dependence using a Helmholtz coil [Figure 1(a)]. Using a fluorescence microscope, they measured the emission intensity of the nanodiamond films and obtained a spectrum versus microwave frequency. This spectrum corresponds to the energy of the electron spins and varies with the magnetic field strength applied to the diamond. Quantum measurements can be achieved by estimating the magnetic field strength from this spectrum. In previous studies, magnetic field estimation has been done by fitting the spectrum with a physical model that takes into account the situation where nanodiamonds are scattered. However, it is difficult to model the experimental environment perfectly, and the physical model cannot reproduce the actual spectrum. Therefore, we have developed a method for estimating the magnetic field without using a physical model by using Gaussian process regression [Fig. 1(b)], a machine learning method. Gaussian process regression is a machine learning method used to find a function that links input data and output variables. In this study, the input data and output variables are mapped to spectra and magnetic field intensities, respectively, and the magnetic field dependence of nanodiamonds measured precisely using a Helmholtz coil is used as training data. Using the obtained function, the magnetic field intensity is estimated using the spectrum not used as training data as test data and compared with the magnetic field intensity generated by the Helmholtz coil (called the true magnetic field intensity in this study) to verify the accuracy of this method.

Figure 1: (a) Schematic of the experimental setup. The large ring around the ring is the Helmholtz coil that controls the magnetic field. It has been calibrated in advance with a high-performance flux meter. The green plate-like object is an antenna to irradiate microwaves to manipulate electron spins, and a cover glass with a nanodiamond film attached to it is fixed with tape. A laser is irradiated through an objective lens to measure the emission of the nanodiamonds. (b) Schematic of machine learning. Spectra of nanodiamonds measured at multiple magnetic field strengths are used as training data. The machine learning method used in this study provides a function that converts spectra to magnetic field intensities.

The results of the magnetic field estimation are shown in Figure 2(a). The true magnetic field strength is systematically changed in the range from 0 μT to 2500 μT. When the magnetic field is estimated from the test data by the conventional method using a physical model, the range of estimation accuracy is inconsistent with the true magnetic field strength under most conditions. On the other hand, the present method, which uses machine learning, produces results that are consistent with the true magnetic field strength. This means that this method can obtain the correct estimation accuracy, which was not possible with the conventional method. Comparing the difference between the true magnetic field strength and the estimated central value, the new method improves the accuracy by up to a factor of 50 compared to the conventional method. We also found that our method can obtain accuracy as high as 1.8 μT (about 1/25th of the geomagnetic field). In addition, we performed a similar validation when nanodiamonds were scattered on a semiconductor silicon substrate instead of a cover glass [Figure 2(b)]. Here, too, the estimation accuracy was correctly estimated, and we succeeded in estimating the magnetic field strength more accurately than with the conventional method. This also demonstrates the applicability of this method to general materials. Figure 2(c) shows the result of localized imaging of the magnetic field generated by the current flowing through a conductor using this method. The magnetic field intensity decreases as one moves away from the conductor, which is consistent with the fitting result based on Ampere's law shown by the solid line. This result means that we have succeeded in accurate magnetic field imaging with high spatial resolution on the micro scale.

Figure 2: (a) Difference between estimated and true magnetic field strength. The (true) magnetic field intensity generated by the Helmholtz coil is compared with the estimated value. For a systematic evaluation, the true magnetic field strength is varied in the range 0 μT ~ 2500 μT. The conventional method using the physical model indicated by the crosses does not include the true magnetic field strength inside the estimation accuracy at almost all measurement points. On the other hand, the present method, which uses machine learning as shown in the circle, includes the true magnetic field within the measurement accuracy at almost all measurement points, resulting in accurate magnetic field estimation. (b) This is the result when a silicon substrate is used instead of a cover glass. Here, too, the range of estimation accuracy is accurately estimated by this method, and the estimated results are consistent with the true magnetic field strength. (c) Results of magnetic field imaging. As shown in the interpolation diagram, this is the result of estimating the magnetic field distribution produced by the current in the conductor. The data shown in the circle can be fitted with high accuracy by a function derived from Ampere's law with the position of the conductor as a parameter. This result means that accurate magnetic field imaging is possible with this method.

Significance
This is the first successful application of machine learning to high-spatial-resolution and accurate magnetic field imaging using nanodiamond films. Since nanodiamond films can be attached to materials of any shape, they can be used for magnetic materials, electronic devices, magnetic organisms, and minerals. This study presents one method for accurately estimating magnetic fields with high spatial resolution using diamond quantum sensors, and will contribute to the development of research in a wide range of fields, including physics, biology, and geology, where local magnetic field measurements are required.

Part of this research was supported in part by Grant-in-Aid for Scientific Research on Innovative Areas (proposed research area) "Control and Function of Quantum Liquid Crystals" (JP19H05826, JP19H05822), Grant-in-Aid for Scientific Research (A) (JP19H00656), Japan Society for the Promotion of Science (JP21K13859), Young Scientists' Research Start Support (JP19K23424, JP22325). This work was supported by technical assistance from the Nanotechnology Platform of the Ministry of Education, Culture, Sports, Science and Technology of Japan. The first author, Mouta Tsukamoto, received research support from Daikin Fellowship (Daikin Industries, Ltd.), FoPM (Forefront Physics and Mathematics Program for World-leading and Smart Innovation (WISE Program), MEXT), and Academic Support Staff (JSPS). Co-author Kensuke Ogawa, a graduate student, has received research support from FoPM and the Japan Society for the Promotion of Science (JSPS) Fellowship Program.

Journals

Journal name	Scientific Reports
Title of paper	"Accurate magnetic field imaging using nanodiamond quantum sensors enhanced by machine learning"
Author(s)	Moeta Tsukamoto∗, Shuji Ito, Kensuke Ogawa, Yuto Ashida, Kento Sasaki∗, and Kensuke Kobayashi∗.
DOI Number	10.1038/s41598-022-18115-w

Terminology

1. Nanodiamond

Refers to nanometer-sized diamond particles. Aqueous solutions of nanodiamond containing lattice defects that emit light are commercially available. Even if the object to be measured is uneven, nanodiamonds can be bonded to its surface simply by dropping the nanodiamond solution on it and allowing it to dry. The present results are based on experiments conducted with nanodiamond products with a particle size of 50 nm purchased from Adámas. ↑up

Note 2 Nitrogen Vacancy Center

Nitrogen vacancy centers are one of the defects that exist in diamond. It refers to a pair in which one carbon atom in the diamond lattice is replaced by a nitrogen atom and the adjacent carbon atom is lost (becomes a vacancy). In particular, in this research, only the NV- state, a negatively charged state, is used. When irradiated with green light, it shows red emission. Since this optical transition is closely related to the electron spin, its spin state can be initialized and read out. ↑up

Note 3 Electron spin

Electrons have an electric charge, but they also have a quantity called spin. Because of this spin, each electron behaves like a small magnet. In this research, we use the fact that the energy of this small magnet changes depending on the magnetic field to measure the magnetic field. ↑up

Note 4 Quantum measurement

This is the use of a system with quantized energy levels to measure physical quantities. In this research, the magnetic field intensity is measured by using levels with quantized electron spins, such as upward and downward. ↑up

Note 5 Helmholtz coil

Refers to a pair of coils used to generate a spatially uniform magnetic field. Six coils are utilized to control the magnetic field intensity in three dimensions. The magnetic field strength is calibrated in advance using a high-precision commercial flux meter. In this study, the estimation accuracy is evaluated based on this magnetic field strength. By combining the results of this calibration with the nanodiamond signal through machine learning, we have succeeded in achieving a high spatial resolution, which is difficult to achieve with ordinary magnetic flux meters. ↑up

Note 6 Nuclear interferometric microscope

This microscope measures surface topography by scanning a microscopic probe. By detecting the interatomic force acting between the tip and the surface to be measured, high spatial resolution of angstroms can be achieved. In this research field, a special diamond tip with a nitrogen vacancy center at the tip is fabricated and used for magnetic field imaging with high spatial resolution. ↑up