Observation of the ${}^1{S}_0$ to ${}^3{D}_1$ clock transition in ${}^{175}{\mathrm{Lu}}^{+}$

We report direct laser spectroscopy of the ${}^1{S}_0$ to ${}^3{D}_1$ highly-forbidden M1 clock transition in ${}^{175}{\mathrm{Lu}}^{+}$. Clock operation is demonstrated on three pairs of Zeeman transitions, one pair from each hyperfine manifold of the ${}^3{D}_1$ term. We measure the hyperfine intervals of the ${}^3{D}_1$ to 10 ppb uncertainty and infer the optical frequency averaged over the three hyperfine transitions to be $353.6399159522\left(6\right)$ THz. The lifetime of the ${}^3{D}_1$ state is inferred to be ${174}_{-32}^{+23}$ hours from the M1 coupling strength.

Figure 1

(a) Level structure of ${\mathrm{Lu}}^{+}$. The 350 nm and 622 nm transitions (dashed) provide optical pumping. The 646 nm transition (solid) provides detection and state preparation. The 848 nm transition (double line) is the highly forbidden M1 clock transition. (b) and (c) Schematic representation of the Paul trap showing the geometry and polarizations of all addressing lasers. Doppler cooling lasers for ${\mathrm{Ba}}^{+}$ (493 nm and 650 nm) are not shown.

Figure 2

The ${}^1{S}_0$ to ${}^3{D}_1$ clock transition in ${}^{175}{\mathrm{Lu}}^{+}$. (a) Measured ${}^3{D}_1$ hyperfine structure and average optical transition frequency of the three hyperfine components. (b) Specific Zeeman transitions interrogated in the reported experiments. The three Zeeman transitions of opposite angular momentum to those shown are also interrogated. The thin solid lines represent the bare hyperfine energies in the absence of the Zeeman effect.

Figure 3

Interrogation of the ${|}^1{S}_0,F=\frac{7}{2},m_F=\frac{7}{2}{\rangle \to |}^3{D}_1,F^{\prime }=\frac{7}{2},m_{F^{\prime }}=\frac{5}{2}\rangle$ clock transition. Each point represents an average of 300 experiments. (a) Rabi flopping is observed by varying the interrogation time. The solid line fit is a sine function with exponentially decaying amplitude. (b) Transition probability when varying the laser frequency for fixed pulse time (1 ms). The fit is a fourier-limited Rabi lineshape with $98\%$ contrast.

Figure 4

Frequency difference between the primary clock laser stabilized to the ${|}^3{D}_1,\frac{9}{2},\pm \frac{9}{2}{\rangle \to |}^1{S}_0,\frac{7}{2},\pm \frac{7}{2}\rangle$ transition and the second clock laser which is stabilized to (a) the ${|}^1{S}_0,\frac{7}{2},\pm \frac{7}{2}{\rangle \to |}^3{D}_1,\frac{7}{2},\pm \frac{5}{2}\rangle$ transition or (b) the ${|}^1{S}_0,\frac{7}{2},\pm \frac{7}{2}{\rangle \to |}^3{D}_1,\frac{5}{2},\pm \frac{5}{2}\rangle$ transition. Discrete frequency jumps are due to a change in the ac-Stark shifts when the two ions swap crystal positions (refer to text).