Rotation Sensing with a Trapped Barium Ion

To date, the best rotation sensors are Sagnac interferometers. The associated phase $\Phi$ due to a rotation rate $\vec{\Omega}$ is proportional to the particle energy $E$ and the enclosed area $\vec{A}$ of the interferometer:$\Phi=\frac{4\pi E}{hc^2}\vec{A}\cdot\vec{\Omega}$. We present an experiment using a ground state Zeeman qubit and a modified version of the recently developed spin-dependent kicks technique [1] to create an interferometer with a single $\rm^{138}Ba^+$ ion in a linear Paul trap ($r_0=1$ cm) [2]. With a trap this large it is difficult to operate in the Lamb-Dicke regime, but the initial ion velocity may only reduce contrast and will not produce an additional phase shift. We will reach sensitivities comparable to other matter-wave interferometers $(\sim 1\ \rm\mu rad \ s^{-1}Hz^{-1/2})$ by taking advantage of the extra energy afforded by using massive particles and the long coherence time of the ion (at least 1 s), allowing it to orbit in the trap many times before closing the interferometer. \begin{thebibliography}{9}\bibitem{S}J. Mizrahi et al., Phys. Rev. Lett.\bf 110\rm, 203001 (2013)\bibitem{u}W. C. Campbell and P. Hamilton, J. Phys. B.\bf 50\rm, 064002 (2017)\end{thebibliography}