Gyroscopes based on nitrogen-vacancy centers in diamond

We propose solid-state gyroscopes based on ensembles of negatively charged nitrogen-vacancy (${\mathrm{NV}}^{-}$) centers in diamond. In one scheme, rotation of the NV${}^{-}$ symmetry axis will induce Berry phase shifts in the ${\mathrm{NV}}^{-}$ electronic ground-state coherences proportional to the solid angle subtended by the symmetry axis. We estimate a sensitivity in the range of $5\times {10}^{-3}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$ in a 1-mm${}^3$ sensor volume using a simple Ramsey sequence. Incorporating dynamical decoupling to suppress dipolar relaxation may yield a sensitivity at the level of ${10}^{-5}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$. 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 ${10}^{-5}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$, however, the lower gyromagnetic ratio of ${}^{14}\mathrm{N}$ nuclei reduces the sensitivity to magnetic-field noise by several orders of magnitude. Reaching ${10}^{-5}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$ would represent an order of magnitude improvement over other compact, solid-state gyroscope technologies.

Figure 1

(a) Ground-state energy levels of NV${}^{-}$ centers in the presence of a magnetic field of several gauss, and accounting for ${}^{14}\mathrm{N}$ hyperfine coupling. Solid, double-headed (red) arrows show the allowed microwave transitions, which preserve the nitrogen spin, $\Delta m_I=0$. (b) ${}^{14}\mathrm{N}$ hyperfine resolved ODMR spectrum as a function of microwave detuning from $D$ for the case of unpolarized (upper trace) and polarized (lower trace) ${}^{14}\mathrm{N}$ spins.

Figure 2

Rotation of diamond about an axis $z^{\prime }$ oriented at an angle $\theta$ with respect to the ${\mathrm{NV}}^{-}$ symmetry axis.

Figure 3

Pulse sequence for a Berry-phase-based gyroscope using resolved ${}^{14}\mathrm{N}$ hyperfine structure in diamond.