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Gyroscopes find wide applications in everyday life from navigation and inertial sensing to rotation sensors in hand-held devices and automobiles. Current devices, based on either atomic or solid-state systems, typically impose a choice between long-time stability and high sensitivity in a miniaturized system. Thanks to their optical properties, nuclear spins associated with NV centers in diamond have been proposed to overcome this challenge. While optical polarization improves these devices' sensitivities, further improvement is needed. Here, we propose a gyroscope protocol based on a two-spin system that includes a spin intrinsically tied to the host material, while the other spin is effectively in an inertial frame. The rotation rate is then extracted by measuring the relative rotation angle between the two spins starting from their population states, which are robust against spin dephasing. Importantly, the relative rotation rate between the two spins is enhanced by their hyperfine coupling by more than an order of magnitude, further boosting the achievable sensitivity. The ultimate sensitivity of the gyroscope is limited by the lifetime of the spin system and is compatible with a broad dynamic range, even in the presence of magnetic noises or control errors due to initialization and qubit manipulations. Our result enables precise measurement of slow rotations and exploration of fundamental physics.
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