Laser-Cooled Mercury Ion Frequency Standard

A stable and accurate frequency standard based on the 40.5 GHz ground-state hyperfine transition in ${}^{199}{\mathrm{Hg}}^{+}$ ions is described. The ions are confined in a cryogenic linear Paul (rf) trap and laser cooled to form a linear crystal. With seven ions and a Ramsey interrogation time of 100 s, the fractional frequency stability is 3.3 $\left(2\right)\times {10}^{-13\mathrm{}}{\tau }^{-1/2\mathrm{}}$ for measurement times $\tau <2\mathrm{h}$. The ground-state hyperfine interval is measured to be 40 507 347 996.841 59 (14) (41) Hz, where the first number in the parentheses is the uncertainty due to statistical and systematic effects, and the second is the uncertainty in the frequency of the time scale to which our standard is compared.