N nuclear spin associated with the nitrogen-vacancy center in diamond, combined with the efficient polarization and measurement of its electronic spin. Although the gyroscope is based on a simple Ramsey interferometry scheme, we use coherent control of the quantum sensor to improve its coherence time and robustness against long-time drifts. Such a sensor can achieve a sensitivity of

\ensuremath{\eta}\ensuremath{\sim}0.5\phantom{\rule{0.28em}{0ex}}(\mathrm{mdeg}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1})/\sqrt{\mathrm{Hz}\phantom{\rule{0.16em}{0ex}}{\mathrm{mm}}^{3}}

while offering enhanced stability in a small footprint. In addition, we exploit the four axes of delocalization of the nitrogen-vacancy center to measure not only the rate of rotation, but also its direction, thus obtaining a compact three-axis gyroscope.

DOI: 10.1103/physreva.86.062104

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{}^{14}

\ensuremath{\eta}\ensuremath{\sim}0.5\phantom{\rule{0.28em}{0ex}}(\mathrm{mdeg}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1})/\sqrt{\mathrm{Hz}\phantom{\rule{0.16em}{0ex}}{\mathrm{mm}}^{3}}

{}^{3}

sensor volume using a simple Ramsey sequence. Incorporating dynamical decoupling to suppress dipolar relaxation may yield a sensitivity at the level of ${10}^{\ensuremath{-}5}$ $\mathrm{rad}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$. With a modified Ramsey scheme, Berry phase shifts in the

{}^{14}\mathrm{N}

hyperfine sublevels would be employed. The projected sensitivity is in the range of ${10}^{\ensuremath{-}5}$ $\mathrm{rad}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$, however, the lower gyromagnetic ratio of

{}^{14}\mathrm{N}

nuclei reduces the sensitivity to magnetic-field noise by several orders of magnitude. Reaching ${10}^{\ensuremath{-}5}$ $\mathrm{rad}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$ would represent an order of magnitude improvement over other compact, solid-state gyroscope technologies.

{}^{14}\mathrm{N}

nuclear spins associated with NV centers act as sensing qubits. We show that the rotation is encoded in a geometric (Berry) phase and identify a near-resonant regime with strongly enhanced phase response. To suppress the resulting nonadiabatic leakage, we introduce a counter-diabatic protocol derived from the Kato gauge potential. This enables robust geometric-phase accumulation and improves the sensitivity by four orders of magnitude relative to the conventional detuned protocol. We further evaluate the achievable sensitivity and the dominant experimental limitations, including decoherence and protocol overhead, thereby establishing a realistic route toward high-performance NV-based solid-state quantum gyroscopes.