Herbert P. Broida Prize: Stable and Accurate Single-Atom Optical Clocks*

Optical clocks based on narrow transitions of single ions have long promised unprecedented stability and accuracy, but only lately has this potential begun to be realized [1-3]. At NIST, two single-ion optical clocks are in operation. A $^{199}$Hg$^{+}$ clock uses a single laser-cooled ion held in a cryogenic rf Paul trap and is based on the $^{2}$S$_{1/2}$ ($F$ = 0) $\leftrightarrow \quad ^{2}$D$_{5/2}$ ($F$ = 2, $m_{F} = 0)$ electric-quadrupole transition at 282 nm. An $^{27}$Al$^{+}$ clock uses a single ion held in a linear trap and is based on the $^{1}$S$_{0} \quad \leftrightarrow \quad ^{3}$P$_{0}$ intercombination line at 267 nm [4]. The burden of cooling, state preparation and state detection of the Al$^{+}$ ion are borne by an auxiliary Be$^{+}$ ion using quantum logic methods [5]. A recent comparison of these two standards achieved a relative fractional frequency instability of less than 7 $\times $ 10$^{-15 }(\tau $/s)$^{-1/2}$, reaching 4 $\times $ 10$^{-17}$ in 30 000. The absolute frequency of the Hg$^{+}$ clock was measured against the cesium fountain standard NIST-F1, and we obtained fractional frequency inaccuracies below 10$^{-15}$. An evaluation of the systematic shifts of the Hg$^{+}$ system in the latest of these measurements returns a total systematic uncertainty of about 3 x 10$^{-17}$ and that of the Al$^{+}$ standard, 2.6 x 10$^{-17}$. We will report the results of measurements conducted over the course of five years and discuss the implications of these results as a constraint to test for the constancy of the fundamental constants that determine atomic transition frequencies [6]. We will also describe the present limitations and planned improvements to the accuracy of the single ion clocks. 1. H.S. Margolis \textit{et al., }Science \textbf{306}, 1355 (2004). 2. T. Schneider, E. Peik, and Chr. Tamm, Phys. Rev. Lett. \textbf{94}, 230801 (2005). 3. W.H. Oskay \textit{et al.}, Phys. Rev. Lett. \textbf{97}, 020801 (2006). 4. P.O. Schmidt \textit{et al., }Science \textbf{309}, 749 (2005). 5. D.J. Wineland \textit{et al.}, \textit{Proc. 6th Symposium on Frequency Standards and Metrology, }P. Gill, ed. (World Scientific, Singapore, 2002) pp. 361-368. 6. T. M. Fortier \textit{et al.,} Phys. Rev. Lett. accepted for publication (2007).