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Nitrogen-vacancy (NV) centers in diamond have become an important tool forquantum technologies. All of these applications rely on long coherence times ofelectron and nuclear spins associated with these centers. Here, we study theenergy level anti-crossings of an NV center in diamond coupled to a first-shell13C nuclear spin in a small static magnetic field. These level anti-crossingsoccur for specific orientations of the static magnetic field due to the strongnon-secular components of the Hamiltonian. At these orientations we observedecoherence-free subspaces, where the electron spin coherence times (T_2* ) are5-7 times longer than those at other orientations. Another interesting propertyat these level anti-crossings is that individual transition amplitudes aredominated by a single component of the magnetic dipole moment. Accordingly,this can be used for vector detection of microwave magnetic fields with asingle NV center. This is particularly important to precisely control thecenter using numerical optimal control techniques.

Level anti-crossings of an NV center in diamond: Decoherence-free subspaces and 3D sensors of microwave magnetic fields