Precision measurement of the ${}^{176}{\mathrm{Lu}}^{+}$ ${}^3{D}_1$ microwave clock transitions

Abstract

We report precision measurement of the unperturbed ${}^3{D}_1$ microwave transition frequencies in ${}^{176}{\mathrm{Lu}}^{+}$ to a fractional uncertainty of $4\times 10^{-14}$. We find the $|F,m_F⟩=|8,0⟩$ to $|7,0⟩$ hyperfine transition frequency to be $10491519945.22882(38)$Hz and the $|7,0⟩$ to $|6,0⟩$ transition frequency to be $11290004289.88161(36)$ Hz. At this precision we are able to observe the hyperfine-mediated effects in the ratio of the quadrupole shifts, from which we can directly infer the residual quadrupole moment after ${}^3{D}_1$ hyperfine averaging. We find a residual quadrupole moment of $-2.48(23)\times 10^{-4}e{a}_0^2$, consistent with a previous assessment using a different and less direct method. With the unperturbed microwave frequencies accurately known, the residual quadrupole shift for a ${}^{176}{\mathrm{Lu}}^{+}$ (${}^3{D}_1$) optical frequency standard can henceforth be readily evaluated to $<10^{-20}$ uncertainty by routine ${}^3{D}_1$ microwave spectroscopy.

8 pages, 5 figures, 1 table