Nuclear spin gyroscope with ¹⁵NV centers in diamond

Nuclear spins in solid-state platforms are promising for building rotation sensors due to their long coherence times. Among these platforms, nitrogen-vacancy centers have attracted considerable attention due to its ambient operating conditions, stability, and compact size. Here we present the use of nitrogen-15 nuclear spins of NV centers in building gyroscopes, benefiting from its simpler energy structure and lack of a nuclear quadrupole term. Nevertheless, when used in conventional spin-based rotation sensing protocols, the ¹⁵N-NV system suffers from challenges in coherence protection and is sensitive to misalignment due to its hyperfine coupling to the NV electronic spin. In our work, we characterize the coherence decay mechanisms of the nuclear spin and develop a coherence protection protocol to address these challenges. We experimentally demonstrate an emulated ¹⁵NV gyroscope by measuring a designed rotation rate pattern and show an order-of-magnitude sensitivity improvement with coherence protection. Furthermore, we theoretically propose a different gyroscope protocol that exploits the properties of ¹⁵N to achieve a gyroscope sensitivity that is ultimately limited by the lifetime of the ¹⁵N-NV system spin system, further enhanced by an order of magnitude (up to three orders of magnitude at large magnetic fields) due to the hyperfine interaction.