Frequency measurement of the ${}^1{\mathrm{S}}_0,F=5\mathrm{/}2\leftrightarrow {}^3{\mathrm{P}}_1,F=7\mathrm{/}2$ transition of ${}^{27}$Al${}^{+}$ via quantum logic spectroscopy with ${}^{40}$Ca${}^{+}$

We perform quantum logic spectroscopy with a ${}^{27}$Al${}^{+}$/${}^{40}$Ca${}^{+}$ mixed ion crystal in a linear Paul trap for a measurement of the $(3s^{2}),^{1}$\mathrm{S}${0} \leftrightarrow , (3s3p),^{3}$\mathrm{P}${1}, F=7/2$intercombinationtransitionin$^{27}$Al$^{+}$. Towards this end, Ramsey spectroscopy is used for probing the transition in ${}^{27}$Al${}^{+}$ and the $(4s^2){\mathrm{S}}_{1\mathrm{/}2}\leftrightarrow (4s3d){\mathrm{D}}_{5\mathrm{/}2}$ clock transition in ${}^{40}$Ca${}^{+}$ in interleaved measurements. By using the precisely measured frequency of the clock transition in ${}^{40}$Ca${}^{+}$ as a frequency reference, we determine the frequency of the intercombination line to be ${\nu }_{{}^1{\mathrm{S}}_0\leftrightarrow {}^3{\mathrm{P}}_1,F=7\mathrm{/}2}$=1122 842 857 334 736(93) Hz and the Land'e g-factor of the excited state to be $g_{{}^3{\mathrm{P}}_1,F=7\mathrm{/}2}$=0.428132(2).