S. M. Brewer

We report the first operation of a Ra$^{+}$ optical clock, a promising high-performance clock candidate. The clock uses a single trapped $^{226}$Ra$^{+}$ ion and operates on the $7s\ ^2S_{1/2}\rightarrow$ $6d\ ^2D_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1$\times10^{-13}$/$\sqrtτ$, where $τ$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be ${Δν/ ν= 9 \times 10^{-16}}$. Using the clock, we realize the first measurement of the ratio of the $D_{5/2}$ state to the $S_{1/2}$ state Landé $g$-factors: $g_{D}/g_{S}$ = 0.5988053(11). A Ra$^{+}$ optical clock could improve limits on the time variation of the fine structure constant, $\dot α/ α$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an $^{27}$Al$^+$ clock to enable a total fractional systematic uncertainty below $10^{-18}$. For this clock, with 38(19) nPa of room temperature H$_2$ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order $10^{-16}$ at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be $-0.6(2.4)\times 10^{-19}$, where the shift is due to collisional heating time-dilation and the uncertainty is dominated by the worst case $\pm π/2$ bound used for collisional phase shift of the $^{27}$Al$^+$ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

We describe an optical atomic clock based on quantum-logic spectroscopy of the $^1$S$_0$ $\leftrightarrow$ $^3$P$_0$ transition in $^{27}$Al$^{+}$ with a systematic uncertainty of ${9.4 \times 10^{-19}}$ and a frequency stability of ${1.2\times10^{-15}/\sqrtτ}$. A $^{25}$Mg$^{+}$ ion is simultaneously trapped with the $^{27}$Al$^{+}$ ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous $^{27}$Al$^{+}$ clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous $^{27}$Al$^{+}$ clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.