Broida Prize Talk: Stable and Accurate Single-Atom Optical Clocks*

The potential for high stability and accuracy of optical clocks based on narrow transitions of single ions has begun to be realized [1-3]. At NIST, we have constructed and are operating two single-ion optical clocks; one based on the $^{2}$S$_{1/2}$ ($F$ = 0) $\leftrightarrow \quad ^{2}$D$_{5/2}$ ($F$ = 2, $m_{F} = 0)$ electric-quadrupole transition ($\lambda $ = 282 nm, $\nu $ = 1.064 PHz) of a single, laser-cooled $^{199}$Hg$^{+}$ ion held in a cryogenic rf Paul trap, and one based on the $^{1}$S$_{0} \quad \leftrightarrow \quad ^{3}$P$_{0}$ intercombination line ($\lambda $ = 267 nm, $\nu $ = 1.124 PHz) of a single $^{27}$Al$^{+}$ ion held in a linear trap [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]. In a recent comparison of these two standards, we have 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 s. We have also compared the frequency of the Hg$^{+}$ optical clock to that of the cesium fountain standard NIST-F1, for which we obtained fractional frequency inaccuracies below 10$^{-15}$. Repeated measurements of the frequency ratios of the clock transitions of all three standards provide intriguing possibilities for laboratory tests of fundamental physics, such as testing for the ``constancy'' of the fundamental constants. 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 present-day temporal variation of the constants [6]. \newline \newline \textbf{References} \newline [1] H.S. Margolis \textit{et al., }Science \textbf{306}, 1355 (2004). \newline [2] T. Schneider, E. Peik, and Chr. Tamm, Phys. Rev. Lett. \textbf{94}, 230801 (2005). \newline [3] W.H. Oskay \textit{et al.}, Phys. Rev. Lett. \textbf{97}, 020801 (2006). \newline [4] P.O. Schmidt \textit{et al., }Science \textbf{309}, 749 (2005). \newline [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. \newline [6] T. M. Fortier \textit{et al.,} Phys. Rev. Lett. accepted for publication (2007).