Estimation of vector static magnetic field by a nitrogen-vacancy center with a single first-shell ¹³ C nuclear (NV– ¹³ C) spin in diamond

Abstract

We suggest an experimental scheme that a single nitrogen-vacancy (NV) center coupled to a nearest neighbor 13 C nucleus as a sensor in diamond can be used to detect a static vector magnetic field. By means of optical detection magnetic resonance (ODMR) technique, both the strength and the direction of the vector field could be determined by relevant resonance frequencies of continuous wave (CW) and Ramsey spectrums. In addition, we give a method that determines the unique one of eight possible hyperfine tensors for an (NV-13 C) system. Finally, we propose an unambiguous method to exclude the symmetrical solution from eight possible vector fields, which correspond to nearly identical resonance frequencies due to their mirror symmetry about 14 N-Vacancy-13 C ( 14 N-V-13 C) plane.

Determination of the Three-Dimensional Magnetic Field Vector Orientation with Nitrogen Vacany Centers in Diamond

“…Another approach uses ensemble measurements with continuous wave readout and frequency multiplexing to determine the ODMR spectra, however it is conceivable that this approach could be extended to the single site level. Moreover, a strongly coupled carbon nuclear spin in close proximity can be used for B-field determination . In contrast, the presented approach here uses single NVs measured in the same confocal volume without any further prerequisite.…”

“…Moreover, a strongly coupled carbon nuclear spin in close proximity can be used for B-field determination. 17 In contrast, the presented approach here uses single NVs measured in the same confocal volume without any further prerequisite. Because of the simplicity of the setup, our technique is generally applicable and thus can be used with most setups without any further technical modification.…”

“…Nevertheless, for an arbitrary magnetic field, the B-field vector solutions given by the separate cones can point toward almost all possible orientations on the sphere. In contrast, the here presented technique allows to narrow this multitude of orientations down to only a very small fraction equivalent to a single axis miss-alignment on the order of 0.4°.Examples of full B-field determinations in the past rely on an NV ensemble where the different [111] axes are in close proximity 15 or on a carbon nuclear spin in close proximity 16.…”

Optical Detection of Paramagnetic Defects in a CVD-grown Diamond

“…In the case of a first shell 13 C, the hyper-fine tensor A can be written as [31] : Diagonalizing the total Hamiltonian, we notice that the quantization axis of the nuclear spin (in the limit γ n B A ij ) is not the same in the manifold of the |m s = 0 state and in the |m s = ±1 states [32], meaning that the nuclear spin is not preserved by the electron spin flip, and gives rise to a splitting of the |m s = 0 → |m s = ±1 transition in 4 distinct lines when the magnetic field is not aligned with the NV center [28].…”

Reconstruction of vector static magnetic field by different axial NV centers using continuous wave optically detected magnetic resonance in diamond

“…[10] To reconstruct the complete information of a static vector magnetic field 𝐵, the azimuth angle should be determined simultaneously. Various methods have been developed to address this issue, including the high-spin system theoretically, [25] the NV center with a single nearest neighbor 13 C system, [26,27] and the techniques of ensemble imaging. [28,29] In our work, we demonstrated a proof-of-principle experiment to reconstruct a static vector magnetic field by three NV sensing spin centers with different crystal axes.…”