Sub-dekalhertz ultraviolet spectroscopy of 199Hg+

Using a laser that is frequency locked to a Fabry-Perot etalon of high finesse and stability, we probe the 5d(10)6s S-2(1/2)(F = 0) <----> 5d(9)6s(2) D-2(5/2)(F = 2) Delta m(F) = 0 electric-quadrupole transition of a single laser-cooled Hg-199(+) 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 x 10(15) Hz), yielding a line Q approximate to 1.6 x 10(14). We perform a preliminary measurement of the 5d(9)6s(2) D-2(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.