Fast Room-Temperature Phase Gate on a Single Nuclear Spin in Diamond*

Nuclear spins support long lived quantum coherence due to weak coupling to the environment, but are difficult to rapidly control using nuclear magnetic resonance as a result of the small nuclear magnetic moment. We demonstrate a fast $\sim 500$\ ns nuclear spin phase gate on a $^{14}$N nuclear spin qubit intrinsic to a nitrogen-vacancy center in high purity diamond [1]. This phase gate is achieved by utilizing electron-nuclear hyperfine interaction. By driving off-resonant Rabi oscillations on the electronic spin, we can generate an arbitrary phase gate on the nuclear spin. We also demonstrate that repeated applications of $\pi$-phase gates can bang-bang decouple the nuclear spin from the environment, locking the spin state for up to 140\ $\mu$s. \\[4pt] [1] S. Sangtawesin, T. O. Brundage, and J. R. Petta, Phys. Rev. Lett. 113, 020506 (2014)