Rotation Sensing with a Trapped Barium Ion

We present progress toward an experiment using a Zeeman qubit and a modified version of the recently developed spin-dependent kicks technique [1] to create an interferometric matter-wave gyroscope with a single $^{138}$Ba$^+$ ion in a linear Paul trap [2]. A rotation rate, $\Omega$ can be extracted by measuring the Sagnac phase: $\Phi=\frac{4\pi E}{hc^2}(N\vec{A})\cdot \vec{\Omega}$, where $E$ is the particle energy, and $N\vec{A}$ is the effective area of the interferometer. In order to reach sensitivities comparable to commercially available gyroscopes (\sim 1 $\mu$rad s$^{-1}$Hz$^{-1/2}$) we take advantage of the increased energy afforded by using massive particles and allowing the ion to orbit in the trap $N$ times before closing the interferometer. With the ion's long coherence time and a secular trap frequency of 10--100 kHz we hope to achieve $N=100$ orbits in the trap. We have trapped and shown coherent control of a Zeeman qubit using a mode-locked Nd:YAG laser. This includes observing both Rabi oscillations and Ramsey fringes using a Raman transition between the qubit states.\\ \\Reference:\\ \\ $[1]$ J. Mizrahi et al., Phys. Rev. Lett. 110, 203001 (2013)\newline $[2]$ W. C. Campbell and P. Hamilton, J. Phys. B. 50, 064002 (2017)