Optically assigned vector magnetometry with nitrogen-vacancy center ensembles in diamond via polarization anisotropy.

The nitrogen-vacancy (NV) center in diamond is a promising platform for quantum magnetometry due to its spin-dependent optical readout and ability to operate under ambient conditions. For vector magnetometry, an ensemble of NV centers aligned along four different crystallographic orientations can be used to determine both the magnitude and direction of a magnetic field via optically detected magnetic resonance (ODMR) spectra. However, due to the symmetry and equivalent crystallographic planes of the diamond lattice, full reconstruction of the magnetic field vector typically requires an external bias field to lift the degeneracy between NV orientations. Here, we demonstrate that this degeneracy can be lifted by illuminating the diamond at an oblique angle and analyzing the resulting polarization-dependent ODMR spectra. The unique dipole orientation of the NV centers enables the unambiguous assignment of ODMR transitions to specific NV axes, and we show that as few as eight measurements are sufficient to reconstruct the full magnetic field vector. Our method enables rapid vector magnetometry of arbitrary magnetic fields without the need to apply or vary a reference field, especially when all the ODMR transitions are well-resolved. This approach opens the door to more compact and portable magnetometers and may facilitate real-time magnetic field imaging in materials science and biological systems.