Sub-dekahertz Ultraviolet Spectroscopy of199Hg+

Using a laser that is frequency locked to a Fabry-Pérot étalon of high finesse and stability, we probe the ${5d}^{10}6s{}_{}{}^2{}_{}{}^{}S_{1/2}^{}{}_{}{}^{}(F=0\mathrm{})\leftrightarrow {5d}^9{6s}^2{}_{}{}^2{}_{}{}^{}D_{5/2}^{}{}_{}{}^{}(F=2\mathrm{})$ $\Delta m_F=0\mathrm{}$ electric-quadrupole transition of a single laser-cooled ${}^{199}{\mathrm{Hg}}^{+}$ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm ( $1.06\times {10}^{15}\mathrm{Hz}$), yielding a line $Q\approx 1.6\times {10}^{14}$. We perform a preliminary measurement of the ${5d}^9{6s}^2{}_{}{}^2{}_{}{}^{}D_{5/2}^{}{}_{}{}^{}$ electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.