Measurement of the (199)Hg+ 5d9 6s2 (2)D(5/2) electric quadrupole moment and a constraint on the quadrupole shift.

The electric-quadrupole moment of the (199)Hg+ 5d9 6s2 (2)D(5/2) state is measured to be theta(D,5/2) = -2.29(8) x 10(-40) C m2. This value was determined by measuring the frequency of the (199)Hg+ 5d10 6s (2)S(1/2) --> 5d9 6s2 (2)D(5/2) optical clock transition for different applied electric-field gradients. An isolated, mechanically stable optical cavity provides a frequency reference for the measurement. We compare the results with theoretical calculations and discuss the implications for the accuracy of an atomic clock based upon this transition. We now expect that the frequency shift caused by the interaction of the quadrupole moment with stray electric-field gradients will not limit the accuracy of the Hg+ optical clock at the 10(-18) level.