Gyroscopes based on nitrogen-vacancy centers in diamond

Abstract

We propose solid-state gyroscopes based on ensembles of negatively charged nitrogen-vacancy (${\mathrm{NV}}^{\ensuremath{-}}$) centers in diamond. In one scheme, rotation of the NV${}^{\ensuremath{-}}$ symmetry axis will induce Berry phase shifts in the ${\mathrm{NV}}^{\ensuremath{-}}$ electronic ground-state coherences proportional to the solid angle subtended by the symmetry axis. We estimate a sensitivity in the range of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ $\mathrm{rad}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$ 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 ${10}^{\ensuremath{-}5}$ $\mathrm{rad}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$. 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.