Gyroscopes based on nitrogen-vacancy centers in diamond

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